Your data matches 70 different statistics following compositions of up to 3 maps.
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Matching statistic: St000254
(load all 106 compositions to match this statistic)
Mapping
Mp00091: Set partitions —rotate increasing⟶ Set partitions
St000254: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => {{1,2}}
 => 1
{{1},{2}}
 => {{1},{2}}
 => 0
{{1,2,3}}
 => {{1,2,3}}
 => 1
{{1,2},{3}}
 => {{1},{2,3}}
 => 1
{{1,3},{2}}
 => {{1,2},{3}}
 => 1
{{1},{2,3}}
 => {{1,3},{2}}
 => 1
{{1},{2},{3}}
 => {{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => {{1,2,3,4}}
 => 1
{{1,2,3},{4}}
 => {{1},{2,3,4}}
 => 1
{{1,2,4},{3}}
 => {{1,2,3},{4}}
 => 1
{{1,2},{3,4}}
 => {{1,4},{2,3}}
 => 2
{{1,2},{3},{4}}
 => {{1},{2,3},{4}}
 => 1
{{1,3,4},{2}}
 => {{1,2,4},{3}}
 => 1
{{1,3},{2,4}}
 => {{1,3},{2,4}}
 => 1
{{1,3},{2},{4}}
 => {{1},{2,4},{3}}
 => 1
{{1,4},{2,3}}
 => {{1,2},{3,4}}
 => 1
{{1},{2,3,4}}
 => {{1,3,4},{2}}
 => 1
{{1},{2,3},{4}}
 => {{1},{2},{3,4}}
 => 1
{{1,4},{2},{3}}
 => {{1,2},{3},{4}}
 => 1
{{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => 1
{{1},{2},{3,4}}
 => {{1,4},{2},{3}}
 => 1
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => 0
Description
The nesting number of a set partition. This is the maximal number of chords in the standard representation of a set partition that mutually nest.
Matching statistic: St001859
(load all 180 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
St001859: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => 1
{{1},{2}}
 => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => 1
{{1,2},{3}}
 => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => 1
{{1},{2,3}}
 => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => 1
{{1,2,3},{4}}
 => [2,3,1,4] => 1
{{1,2,4},{3}}
 => [2,4,3,1] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => 1
{{1,3},{2,4}}
 => [3,4,1,2] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => 1
{{1},{2,3},{4}}
 => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => 0
Description
The number of factors of the Stanley symmetric function associated with a permutation. For example, the Stanley symmetric function of $\pi=321645$ equals $20 m_{1,1,1,1,1} + 11 m_{2,1,1,1} + 6 m_{2,2,1} + 4 m_{3,1,1} + 2 m_{3,2} + m_{4,1} = (m_{1,1} + m_{2})(2 m_{1,1,1} + m_{2,1}).$
Matching statistic: St000162
(load all 25 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000162: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => 1
{{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => 1
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => [2,3,1] => 1
{{1},{2,3}}
 => [1,3,2] => [3,1,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [3,2,4,1] => 1
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => 1
{{1,2,4},{3}}
 => [2,4,3,1] => [4,2,3,1] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [2,3,4,1] => 1
{{1,3},{2,4}}
 => [3,4,1,2] => [4,3,1,2] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [2,3,1,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [3,4,2,1] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [3,1,4,2] => 1
{{1},{2,3},{4}}
 => [1,3,2,4] => [3,1,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,4,3,1] => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => [4,1,3,2] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
Description
The number of nontrivial cycles in the cycle decomposition of a permutation. This statistic is equal to the difference of the number of cycles of $\pi$ (see [[St000031]]) and the number of fixed points of $\pi$ (see [[St000022]]).
Matching statistic: St000253
(load all 97 compositions to match this statistic)
Mapping
Mp00176: Set partitions —rotate decreasing⟶ Set partitions
Mp00219: Set partitions —inverse Yip⟶ Set partitions
St000253: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => {{1,2}}
 => {{1,2}}
 => 1
{{1},{2}}
 => {{1},{2}}
 => {{1},{2}}
 => 0
{{1,2,3}}
 => {{1,2,3}}
 => {{1,2,3}}
 => 1
{{1,2},{3}}
 => {{1,3},{2}}
 => {{1},{2,3}}
 => 1
{{1,3},{2}}
 => {{1},{2,3}}
 => {{1,3},{2}}
 => 1
{{1},{2,3}}
 => {{1,2},{3}}
 => {{1,2},{3}}
 => 1
{{1},{2},{3}}
 => {{1},{2},{3}}
 => {{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => {{1,2,3,4}}
 => {{1,2,3,4}}
 => 1
{{1,2,3},{4}}
 => {{1,2,4},{3}}
 => {{1,2},{3,4}}
 => 1
{{1,2,4},{3}}
 => {{1,3,4},{2}}
 => {{1},{2,3,4}}
 => 1
{{1,2},{3,4}}
 => {{1,4},{2,3}}
 => {{1,3},{2,4}}
 => 2
{{1,2},{3},{4}}
 => {{1,4},{2},{3}}
 => {{1},{2},{3,4}}
 => 1
{{1,3,4},{2}}
 => {{1},{2,3,4}}
 => {{1,3,4},{2}}
 => 1
{{1,3},{2,4}}
 => {{1,3},{2,4}}
 => {{1,4},{2,3}}
 => 1
{{1,3},{2},{4}}
 => {{1},{2,4},{3}}
 => {{1},{2,4},{3}}
 => 1
{{1,4},{2,3}}
 => {{1,2},{3,4}}
 => {{1,2,4},{3}}
 => 1
{{1},{2,3,4}}
 => {{1,2,3},{4}}
 => {{1,2,3},{4}}
 => 1
{{1},{2,3},{4}}
 => {{1,2},{3},{4}}
 => {{1,2},{3},{4}}
 => 1
{{1,4},{2},{3}}
 => {{1},{2},{3,4}}
 => {{1,4},{2},{3}}
 => 1
{{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => {{1},{2,3},{4}}
 => 1
{{1},{2},{3,4}}
 => {{1},{2,3},{4}}
 => {{1,3},{2},{4}}
 => 1
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => 0
Description
The crossing number of a set partition. This is the maximal number of chords in the standard representation of a set partition, that mutually cross.
Matching statistic: St000374
(load all 22 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
St000374: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => 1
{{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => 1
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => 1
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,2,3,1] => 1
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => 1
{{1,2,4},{3}}
 => [2,4,3,1] => [4,3,2,1] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [4,2,3,1] => 1
{{1,3},{2,4}}
 => [3,4,1,2] => [4,3,2,1] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => 1
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,3,2,1] => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
Description
The number of exclusive right-to-left minima of a permutation. This is the number of right-to-left minima that are not left-to-right maxima. This is also the number of non weak exceedences of a permutation that are also not mid-points of a decreasing subsequence of length 3. Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j < j$ and there do not exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$. See also [[St000213]] and [[St000119]].
Matching statistic: St000390
(load all 18 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
St000390: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => 1 => 1
{{1},{2}}
 => [1,2] => 0 => 0
{{1,2,3}}
 => [2,3,1] => 01 => 1
{{1,2},{3}}
 => [2,1,3] => 10 => 1
{{1,3},{2}}
 => [3,2,1] => 11 => 1
{{1},{2,3}}
 => [1,3,2] => 01 => 1
{{1},{2},{3}}
 => [1,2,3] => 00 => 0
{{1,2,3,4}}
 => [2,3,4,1] => 001 => 1
{{1,2,3},{4}}
 => [2,3,1,4] => 010 => 1
{{1,2,4},{3}}
 => [2,4,3,1] => 011 => 1
{{1,2},{3,4}}
 => [2,1,4,3] => 101 => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => 100 => 1
{{1,3,4},{2}}
 => [3,2,4,1] => 011 => 1
{{1,3},{2,4}}
 => [3,4,1,2] => 001 => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => 110 => 1
{{1,4},{2,3}}
 => [4,3,2,1] => 111 => 1
{{1},{2,3,4}}
 => [1,3,4,2] => 001 => 1
{{1},{2,3},{4}}
 => [1,3,2,4] => 010 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => 011 => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => 011 => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => 001 => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => 000 => 0
Description
The number of runs of ones in a binary word.
Matching statistic: St000996
(load all 16 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
St000996: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => 1
{{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => 1
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => 1
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,2,3,1] => 1
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => 1
{{1,2,4},{3}}
 => [2,4,3,1] => [4,3,2,1] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [4,2,3,1] => 1
{{1,3},{2,4}}
 => [3,4,1,2] => [4,3,2,1] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => 1
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,3,2,1] => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
Description
The number of exclusive left-to-right maxima of a permutation. This is the number of left-to-right maxima that are not right-to-left minima.
Matching statistic: St001280
(load all 10 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
St001280: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2]
 => 1
{{1},{2}}
 => [1,2] => [1,1]
 => 0
{{1,2,3}}
 => [2,3,1] => [2,1]
 => 1
{{1,2},{3}}
 => [2,1,3] => [2,1]
 => 1
{{1,3},{2}}
 => [3,2,1] => [3]
 => 1
{{1},{2,3}}
 => [1,3,2] => [2,1]
 => 1
{{1},{2},{3}}
 => [1,2,3] => [1,1,1]
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => [2,1,1]
 => 1
{{1,2,3},{4}}
 => [2,3,1,4] => [2,1,1]
 => 1
{{1,2,4},{3}}
 => [2,4,3,1] => [3,1]
 => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,2]
 => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,1]
 => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [3,1]
 => 1
{{1,3},{2,4}}
 => [3,4,1,2] => [2,1,1]
 => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,1]
 => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [4]
 => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [2,1,1]
 => 1
{{1},{2,3},{4}}
 => [1,3,2,4] => [2,1,1]
 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [3,1]
 => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => [3,1]
 => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [2,1,1]
 => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,1,1,1]
 => 0
Description
The number of parts of an integer partition that are at least two.
Matching statistic: St001333
(load all 14 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001333: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => ([(0,1)],2)
 => 1
{{1},{2}}
 => [1,2] => ([],2)
 => 0
{{1,2,3}}
 => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
{{1,2},{3}}
 => [2,1,3] => ([(1,2)],3)
 => 1
{{1,3},{2}}
 => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
{{1},{2,3}}
 => [1,3,2] => ([(1,2)],3)
 => 1
{{1},{2},{3}}
 => [1,2,3] => ([],3)
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
{{1,2,3},{4}}
 => [2,3,1,4] => ([(1,3),(2,3)],4)
 => 1
{{1,2,4},{3}}
 => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1,2},{3,4}}
 => [2,1,4,3] => ([(0,3),(1,2)],4)
 => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => ([(2,3)],4)
 => 1
{{1,3,4},{2}}
 => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1,3},{2,4}}
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => 1
{{1,4},{2,3}}
 => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1},{2,3,4}}
 => [1,3,4,2] => ([(1,3),(2,3)],4)
 => 1
{{1},{2,3},{4}}
 => [1,3,2,4] => ([(2,3)],4)
 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => ([(2,3)],4)
 => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => ([],4)
 => 0
Description
The cardinality of a minimal edge-isolating set of a graph. Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$. This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains only the graph with one edge.
Matching statistic: St001393
(load all 14 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001393: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => ([(0,1)],2)
 => 1
{{1},{2}}
 => [1,2] => ([],2)
 => 0
{{1,2,3}}
 => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
{{1,2},{3}}
 => [2,1,3] => ([(1,2)],3)
 => 1
{{1,3},{2}}
 => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
{{1},{2,3}}
 => [1,3,2] => ([(1,2)],3)
 => 1
{{1},{2},{3}}
 => [1,2,3] => ([],3)
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
{{1,2,3},{4}}
 => [2,3,1,4] => ([(1,3),(2,3)],4)
 => 1
{{1,2,4},{3}}
 => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1,2},{3,4}}
 => [2,1,4,3] => ([(0,3),(1,2)],4)
 => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => ([(2,3)],4)
 => 1
{{1,3,4},{2}}
 => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1,3},{2,4}}
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => 1
{{1,4},{2,3}}
 => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1},{2,3,4}}
 => [1,3,4,2] => ([(1,3),(2,3)],4)
 => 1
{{1},{2,3},{4}}
 => [1,3,2,4] => ([(2,3)],4)
 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => ([(2,3)],4)
 => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => ([],4)
 => 0
Description
The induced matching number of a graph. An induced matching of a graph is a set of independent edges which is an induced subgraph. This statistic records the maximal number of edges in an induced matching.
The following 60 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001665The number of pure excedances of a permutation. St001737The number of descents of type 2 in a permutation. St001261The Castelnuovo-Mumford regularity of a graph. St000021The number of descents of a permutation. St000035The number of left outer peaks of a permutation. St000245The number of ascents of a permutation. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000354The number of recoils of a permutation. St000659The number of rises of length at least 2 of a Dyck path. St000670The reversal length of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000703The number of deficiencies of a permutation. St000834The number of right outer peaks of a permutation. St000884The number of isolated descents of a permutation. St000919The number of maximal left branches of a binary tree. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001340The cardinality of a minimal non-edge isolating set of a graph. St001354The number of series nodes in the modular decomposition of a graph. St001489The maximum of the number of descents and the number of inverse descents. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001729The number of visible descents of a permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001928The number of non-overlapping descents in a permutation. St000258The burning number of a graph. St000325The width of the tree associated to a permutation. St000451The length of the longest pattern of the form k 1 2. St000470The number of runs in a permutation. St001498The normalised height of a Nakayama algebra with magnitude 1. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St000455The second largest eigenvalue of a graph if it is integral. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000284The Plancherel distribution on integer partitions. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001128The exponens consonantiae of a partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000264The girth of a graph, which is not a tree. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000929The constant term of the character polynomial of an integer partition. St001568The smallest positive integer that does not appear twice in the partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001060The distinguishing index of a graph. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000681The Grundy value of Chomp on Ferrers diagrams. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000941The number of characters of the symmetric group whose value on the partition is even.