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Your data matches 75 different statistics following compositions of up to 3 maps.
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Matching statistic: St000175
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000175: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000175: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],3)
=> [3,3]
=> [3]
=> 0
([(2,3)],4)
=> [4,4,4]
=> [4,4]
=> 0
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [3]
=> 0
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [3]
=> 0
([(0,3),(1,2)],4)
=> [4,2]
=> [2]
=> 0
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2]
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2]
=> 0
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [15]
=> 0
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [4,4]
=> 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [3]
=> 0
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [5]
=> 0
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2]
=> 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2]
=> 0
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2]
=> 0
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [5,5,5]
=> 0
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [5]
=> 0
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [3]
=> 0
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [5]
=> 0
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2]
=> 0
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [15]
=> 0
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [3]
=> 0
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [10]
=> 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [4]
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [6]
=> 0
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [4,4]
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [4,4]
=> 0
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [5,5]
=> 0
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [4]
=> 0
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [5,5,5]
=> 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2]
=> 0
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [10]
=> 0
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [4,4]
=> 0
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [4,3]
=> 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [4]
=> 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [6]
=> 0
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [3]
=> 0
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [4]
=> 0
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [5]
=> 0
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [2]
=> 0
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [15]
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [3]
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [10]
=> 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [4]
=> 0
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [6]
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [4,4]
=> 0
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [5]
=> 0
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [5,5]
=> 0
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> 0
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [15]
=> 0
Description
Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape.
Given a partition $\lambda$ with $r$ parts, the number of semi-standard Young-tableaux of shape $k\lambda$ and boxes with values in $[r]$ grows as a polynomial in $k$. This follows by setting $q=1$ in (7.105) on page 375 of [1], which yields the polynomial
$$p(k) = \prod_{i < j}\frac{k(\lambda_j-\lambda_i)+j-i}{j-i}.$$
The statistic of the degree of this polynomial.
For example, the partition $(3, 2, 1, 1, 1)$ gives
$$p(k) = \frac{-1}{36} (k - 3) (2k - 3) (k - 2)^2 (k - 1)^3$$
which has degree 7 in $k$. Thus, $[3, 2, 1, 1, 1] \mapsto 7$.
This is the same as the number of unordered pairs of different parts, which follows from:
$$\deg p(k)=\sum_{i < j}\begin{cases}1& \lambda_j \neq \lambda_i\\0&\lambda_i=\lambda_j\end{cases}=\sum_{\stackrel{i < j}{\lambda_j \neq \lambda_i}} 1$$
Matching statistic: St000278
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000278: Integer partitions ⟶ ℤResult quality: 89% ●values known / values provided: 89%●distinct values known / distinct values provided: 100%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000278: Integer partitions ⟶ ℤResult quality: 89% ●values known / values provided: 89%●distinct values known / distinct values provided: 100%
Values
([],3)
=> [3,3]
=> [3]
=> 1 = 0 + 1
([(2,3)],4)
=> [4,4,4]
=> [4,4]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [3]
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [3]
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> [4,2]
=> [2]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2]
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2]
=> 1 = 0 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [4,4]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [3]
=> 1 = 0 + 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [5]
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2]
=> 1 = 0 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2]
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2]
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [5]
=> 1 = 0 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [3]
=> 1 = 0 + 1
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [5]
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2]
=> 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [3]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [10]
=> 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [4]
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [6]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [4,4]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [4,4]
=> 1 = 0 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [5,5]
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [4]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [10]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [4,4]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [4,3]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [4]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [6]
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [3]
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [4]
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [5]
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [2]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [3]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [10]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [4]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [6]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [4,4]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [5]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [5,5]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [2]
=> 1 = 0 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [2]
=> 1 = 0 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [10]
=> 1 = 0 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [4,4]
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [4]
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [6]
=> 1 = 0 + 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [3]
=> 1 = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> ? = 0 + 1
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7)
=> [9,8,7]
=> [8,7]
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7)
=> [9,8,7]
=> [8,7]
=> ? = 1 + 1
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
=> [15,15]
=> [15]
=> ? = 0 + 1
([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> ? = 0 + 1
([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
=> [7,7,7]
=> [7,7]
=> ? = 0 + 1
([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> ? = 0 + 1
([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> ? = 0 + 1
([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> ? = 0 + 1
Description
The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions.
This is the multinomial of the multiplicities of the parts, see [1].
This is the same as $m_\lambda(x_1,\dotsc,x_k)$ evaluated at $x_1=\dotsb=x_k=1$,
where $k$ is the number of parts of $\lambda$.
An explicit formula is $\frac{k!}{m_1(\lambda)! m_2(\lambda)! \dotsb m_k(\lambda) !}$
where $m_i(\lambda)$ is the number of parts of $\lambda$ equal to $i$.
Matching statistic: St000225
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000225: Integer partitions ⟶ ℤResult quality: 89% ●values known / values provided: 89%●distinct values known / distinct values provided: 100%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000225: Integer partitions ⟶ ℤResult quality: 89% ●values known / values provided: 89%●distinct values known / distinct values provided: 100%
Values
([],3)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0
([(2,3)],4)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 0
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0
([(0,3),(1,2)],4)
=> [4,2]
=> [2]
=> [1,1]
=> 0
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2]
=> [1,1]
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2]
=> [1,1]
=> 0
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2]
=> [1,1]
=> 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2]
=> [1,1]
=> 0
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 0
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 0
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [4]
=> [1,1,1,1]
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [4,4]
=> [2,2,2,2]
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 0
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [5,5]
=> [2,2,2,2,2]
=> 0
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [4]
=> [1,1,1,1]
=> 0
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> [1,1]
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 0
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 0
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [4,4]
=> [2,2,2,2]
=> 0
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [4,3]
=> [2,2,2,1]
=> 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [4]
=> [1,1,1,1]
=> 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [3]
=> [1,1,1]
=> 0
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [4]
=> [1,1,1,1]
=> 0
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [2]
=> [1,1]
=> 0
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [4]
=> [1,1,1,1]
=> 0
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [4,4]
=> [2,2,2,2]
=> 0
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [5,5]
=> [2,2,2,2,2]
=> 0
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 0
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 0
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 0
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [4,4]
=> [2,2,2,2]
=> 0
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [4]
=> [1,1,1,1]
=> 0
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0
([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7)
=> [9,8,7]
=> [8,7]
=> [2,2,2,2,2,2,2,1]
=> ? = 1
([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7)
=> [9,8,7]
=> [8,7]
=> [2,2,2,2,2,2,2,1]
=> ? = 1
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0
([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0
([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0
([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0
([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0
([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0
([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0
([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0
Description
Difference between largest and smallest parts in a partition.
Matching statistic: St001128
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001128: Integer partitions ⟶ ℤResult quality: 89% ●values known / values provided: 89%●distinct values known / distinct values provided: 100%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001128: Integer partitions ⟶ ℤResult quality: 89% ●values known / values provided: 89%●distinct values known / distinct values provided: 100%
Values
([],3)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(2,3)],4)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> [4,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 0 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [4]
=> [1,1,1,1]
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 0 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [5,5]
=> [2,2,2,2,2]
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [4]
=> [1,1,1,1]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [4,3]
=> [2,2,2,1]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [4]
=> [1,1,1,1]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [4]
=> [1,1,1,1]
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [4]
=> [1,1,1,1]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [5,5]
=> [2,2,2,2,2]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 0 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1 = 0 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [4]
=> [1,1,1,1]
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 0 + 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0 + 1
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0 + 1
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0 + 1
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0 + 1
([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7)
=> [9,8,7]
=> [8,7]
=> [2,2,2,2,2,2,2,1]
=> ? = 1 + 1
([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7)
=> [9,8,7]
=> [8,7]
=> [2,2,2,2,2,2,2,1]
=> ? = 1 + 1
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0 + 1
([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
=> [15,15]
=> [15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 0 + 1
([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
=> [3,3,3,3,3,3]
=> [3,3,3,3,3]
=> [5,5,5]
=> ? = 0 + 1
([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)
=> [5,5,5,5]
=> [5,5,5]
=> [3,3,3,3,3]
=> ? = 0 + 1
([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0 + 1
([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0 + 1
([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0 + 1
([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
=> [7,7,7]
=> [7,7]
=> [2,2,2,2,2,2,2]
=> ? = 0 + 1
Description
The exponens consonantiae of a partition.
This is the quotient of the least common multiple and the greatest common divior of the parts of the partiton. See [1, Caput sextum, §19-§22].
Matching statistic: St000057
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St000057: Standard tableaux ⟶ ℤResult quality: 33% ●values known / values provided: 43%●distinct values known / distinct values provided: 33%
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St000057: Standard tableaux ⟶ ℤResult quality: 33% ●values known / values provided: 43%●distinct values known / distinct values provided: 33%
Values
([],3)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(2,3)],4)
=> [4,4,4]
=> [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
=> [[1,5,9],[2,6,10],[3,7,11],[4,8,12]]
=> ? = 0
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(0,3),(1,2)],4)
=> [4,2]
=> [[1,2,3,4],[5,6]]
=> [[1,5],[2,6],[3],[4]]
=> 0
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [[1,2,3],[4,5]]
=> [[1,4],[2,5],[3]]
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 0
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
=> [[1,5,9],[2,6,10],[3,7,11],[4,8,12]]
=> ? = 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [[1,2,3,4],[5,6]]
=> [[1,5],[2,6],[3],[4]]
=> 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [[1,2,3],[4,5]]
=> [[1,4],[2,5],[3]]
=> 0
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]
=> [[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]]
=> ? = 0
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 0
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> 0
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
=> [[1,5,9],[2,6,10],[3,7,11],[4,8,12]]
=> ? = 0
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25]]
=> [[1,16,21],[2,17,22],[3,18,23],[4,19,24],[5,20,25],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]]
=> ? = 0
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [[1,2,3,4,5],[6,7,8,9]]
=> [[1,6],[2,7],[3,8],[4,9],[5]]
=> 0
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [[1,2,3],[4,5]]
=> [[1,4],[2,5],[3]]
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]
=> [[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 0
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 0
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [[1,2,3,4],[5,6,7,8],[9,10,11]]
=> [[1,5,9],[2,6,10],[3,7,11],[4,8]]
=> ? = 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> 0
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [[1,2,3,4,5],[6,7,8]]
=> [[1,6],[2,7],[3,8],[4],[5]]
=> 0
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [[1,2,3,4,5],[6,7,8,9]]
=> [[1,6],[2,7],[3,8],[4,9],[5]]
=> 0
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [[1,2,3,4],[5,6]]
=> [[1,5],[2,6],[3],[4]]
=> 0
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 0
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 0
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25]]
=> [[1,16,21],[2,17,22],[3,18,23],[4,19,24],[5,20,25],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]]
=> ? = 0
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]
=> [[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]]
=> ? = 0
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 0
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 0
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 0
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 0
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> 0
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> 0
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> 0
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18]]
=> [[1,4,7,10,13,16],[2,5,8,11,14,17],[3,6,9,12,15,18]]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> 0
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 0
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]]
=> [[1,9],[2,10],[3,11],[4,12],[5,13],[6,14],[7,15],[8,16]]
=> ? = 0
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [4,2]
=> [[1,2,3,4],[5,6]]
=> [[1,5],[2,6],[3],[4]]
=> 0
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
=> [[1,5,9],[2,6,10],[3,7,11],[4,8,12]]
=> ? = 0
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]
=> [[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]]
=> ? = 0
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[1,4],[2,5],[3,6]]
=> 0
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [[1,2,3,4,5,6,7,8],[9,10,11,12],[13,14]]
=> ?
=> ? = 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [[1,2,3,4,5,6],[7,8],[9,10]]
=> [[1,7,9],[2,8,10],[3],[4],[5],[6]]
=> 0
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> [3,2]
=> [[1,2,3],[4,5]]
=> [[1,4],[2,5],[3]]
=> 0
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> [14,2]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14],[15,16]]
=> ?
=> ? = 0
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12]]
=> [[1,11],[2,12],[3],[4],[5],[6],[7],[8],[9],[10]]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
=> [8,8]
=> [[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]]
=> [[1,9],[2,10],[3,11],[4,12],[5,13],[6,14],[7,15],[8,16]]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [[1,2,3,4],[5,6,7,8],[9,10],[11,12]]
=> [[1,5,9,11],[2,6,10,12],[3,7],[4,8]]
=> ? = 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [[1,2,3,4,5,6],[7,8],[9,10]]
=> [[1,7,9],[2,8,10],[3],[4],[5],[6]]
=> 0
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [[1,2],[3,4],[5,6],[7,8]]
=> [[1,3,5,7],[2,4,6,8]]
=> 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [[1,2,3,4],[5,6,7,8]]
=> [[1,5],[2,6],[3,7],[4,8]]
=> 0
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]
=> [[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]]
=> ? = 0
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 0
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]
=> [[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]]
=> ? = 0
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [4,4,4]
=> [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
=> [[1,5,9],[2,6,10],[3,7,11],[4,8,12]]
=> ? = 0
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 0
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18]]
=> [[1,4,7,10,13,16],[2,5,8,11,14,17],[3,6,9,12,15,18]]
=> ? = 0
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> 0
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)
=> [4,4,3]
=> [[1,2,3,4],[5,6,7,8],[9,10,11]]
=> [[1,5,9],[2,6,10],[3,7,11],[4,8]]
=> ? = 1
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)
=> [4,4,3]
=> [[1,2,3,4],[5,6,7,8],[9,10,11]]
=> [[1,5,9],[2,6,10],[3,7,11],[4,8]]
=> ? = 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> [8,8]
=> [[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]]
=> [[1,9],[2,10],[3,11],[4,12],[5,13],[6,14],[7,15],[8,16]]
=> ? = 0
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)
=> [13,2]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13],[14,15]]
=> ?
=> ? = 0
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
=> [8,3]
=> [[1,2,3,4,5,6,7,8],[9,10,11]]
=> [[1,9],[2,10],[3,11],[4],[5],[6],[7],[8]]
=> ? = 0
Description
The Shynar inversion number of a standard tableau.
Shynar's inversion number is the number of inversion pairs in a standard Young tableau, where an inversion pair is defined as a pair of integers (x,y) such that y > x and y appears strictly southwest of x in the tableau.
Matching statistic: St001193
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001193: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001193: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Values
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 0
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 0
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 0
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> ? = 0
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 0
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0]
=> ? = 0
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> 0
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 0
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> 0
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> 0
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 0
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 0
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0]
=> ? = 0
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> ? = 0
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 0
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 0
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 0
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 0
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> ? = 0
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 0
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0]
=> ? = 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
=> ? = 0
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 0
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> [14,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> ?
=> ? = 0
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> ? = 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
=> ? = 0
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 0
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> ? = 0
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 0
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> ? = 0
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 0
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? = 0
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> 0
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 0
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 0
Description
The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module.
Matching statistic: St000964
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St000964: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St000964: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Values
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> [14,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> ?
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
Description
Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra.
Matching statistic: St000965
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St000965: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St000965: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Values
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> [14,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> ?
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
Description
The sum of the dimension of Ext^i(D(A),A) for i=1,...,g when g denotes the global dimension of the corresponding LNakayama algebra.
Matching statistic: St000999
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St000999: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St000999: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Values
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> [14,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> ?
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
Description
Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001006
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001006: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001006: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 67%
Values
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(2,3),(3,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
=> [14,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> ?
=> ? = 0 + 1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 1 = 0 + 1
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 1 = 0 + 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> [8,8]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 0 + 1
Description
Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path.
The following 65 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001191Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001568The smallest positive integer that does not appear twice in the partition. St000781The number of proper colouring schemes of a Ferrers diagram. St001095The number of non-isomorphic posets with precisely one further covering relation. St000914The sum of the values of the Möbius function of a poset. St001890The maximum magnitude of the Möbius function of a poset. St000379The number of Hamiltonian cycles in a graph. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001462The number of factors of a standard tableaux under concatenation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001722The number of minimal chains with small intervals between a binary word and the top element. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000456The monochromatic index of a connected graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001060The distinguishing index of a graph. St001118The acyclic chromatic index of a graph. St001545The second Elser number of a connected graph. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St001301The first Betti number of the order complex associated with the poset. St000908The length of the shortest maximal antichain in a poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000298The order dimension or Dushnik-Miller dimension of a poset. St001563The value of the power-sum symmetric function evaluated at 1. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001597The Frobenius rank of a skew partition. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St001846The number of elements which do not have a complement in the lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001618The cardinality of the Frattini sublattice of a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001877Number of indecomposable injective modules with projective dimension 2. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001875The number of simple modules with projective dimension at most 1. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001624The breadth of a lattice. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
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