**There are 6 pending statistics**:

Identifier

St000240:
Permutations ⟶ ℤ

Values

No modified entries

Description

The number of indices that are not small excedances.

A small excedance is an index $i$ for which $\pi_i \neq i+1$.

A small excedance is an index $i$ for which $\pi_i \neq i+1$.

Diff Description

The number of indices that are not small excedances.

A small excedance is an index i for which \pi_i \neq i+1.

A small excedance is an index i for which \pi_i \neq i+1.

Code

def statistic(pi): return sum( Integer(1) for i in range(len(pi)) if pi[i] != i+2 )

Created

Feb 26, 2015 at 21:04 by

**Christian Stump**Updated

May 22, 2023 at 23:20 by

**Will Dowling**
Identifier

St000238:
Permutations ⟶ ℤ

Values

No modified entries

Description

The number of indices that are not small weak excedances.

A small weak excedance is an index $i$ such that $\pi_i \notin \{i,i+1\}$.

A small weak excedance is an index $i$ such that $\pi_i \notin \{i,i+1\}$.

Diff Description

The number of indices that are not small weak excedances.

A small weak excedance is an index i such that \pi_i \notin \{i,i+1\}.

A small weak excedance is an index i such that \pi_i \notin \{i,i+1\}.

References

[1] Li, Y. Ménage Numbers and Ménage Permutations arXiv:1502.06068

Diff References

[1] Li, Y. Ménage Numbers and Ménage Permutations [[arXiv:1502.06068]]

Code

def statistic(pi): return sum( 1 for i in range(len(pi)) if pi[i] not in [i+1,i+2] )

Created

Feb 24, 2015 at 13:12 by

**Christian Stump**Updated

May 22, 2023 at 23:18 by

**Will Dowling**
2 Comments (hide)

Martin Rubey

23 May 8:56

23 May 8:56

I think there is a typo (
eq should be =)

Christian Stump

23 May 9:05

23 May 9:05

"\
eq should be ="

Identifier

St000235:
Permutations ⟶ ℤ

Values

No modified entries

Description

The number of indices that are not cyclical small weak excedances.

A cyclical small weak excedance is an index $i$ such that $\pi_i \neq i+1$ considered cyclically.

A cyclical small weak excedance is an index $i$ such that $\pi_i \neq i+1$ considered cyclically.

Diff Description

The number of indices that are not cyclical small weak excedances.

A cyclical small weak excedance is an index i such that \pi_i \neq i+1 considered cyclically.~~
~~

A cyclical small weak excedance is an index i such that \pi_i \neq i+1 considered cyclically.

References

[1] Li, Y. Ménage Numbers and Ménage Permutations arXiv:1502.06068

Diff References

[1] Li, Y. Ménage Numbers and Ménage Permutations [[arXiv:1502.06068]]

Code

def statistic(pi): n = len(pi) return sum( 1 for i in range(n) if pi[i] != ( (i+1) % n + 1 ) )

Created

Feb 24, 2015 at 13:16 by

**Christian Stump**Updated

May 22, 2023 at 23:17 by

**Will Dowling**
Identifier

St001288:
Permutations ⟶ ℤ

Values

No modified entries

Description

The number of column-product over-primes.

This is the number of indices $i$ such that $i\pi(i)+1$ is prime.

This is the number of indices $i$ such that $i\pi(i)+1$ is prime.

Diff Description

The number of ~~primes obtained by multiplying ~~column-product over-pr~~e~~im~~age and image of a permutation and adding on~~es.

This is the number of indices i such that i\pi(i)+1 is prime.

This is the number of indices i such that i\pi(i)+1 is prime.

References

[1] Sun, Z.-W. Primes arising from permutations MathOverflow:315259

Code

def statistic(pi): return sum(1 for i in pi if is_prime(i*pi(i) + 1))

Created

Nov 14, 2018 at 09:02 by

**Martin Rubey**Updated

May 22, 2023 at 22:56 by

**Will Dowling**
1 Comments (hide)

Martin Rubey

23 May 8:59

23 May 8:59

This is hard to read. Also, the first line should always contain a hint about which collection the statistic is in, eg. "of a permutation". Why "column"?

Identifier

St001287:
Permutations ⟶ ℤ

Values

No modified entries

Description

The number of column-product almost-primes.

This is the number of indices $i$ such that $i\pi(i)-1$ is prime. Note that the numbers $0$ and $1$ may arise, but are not prime.

This is the number of indices $i$ such that $i\pi(i)-1$ is prime. Note that the numbers $0$ and $1$ may arise, but are not prime.

Diff Description

The number of ~~primes obtained by multiplying ~~column-product almost-pr~~e~~im~~age and image of a permutation and subtracting one.
~~

es.

This is the number of indices i such that i\pi(i)-1 is prime. Note that the numbers 0 and 1 may arise, but are not prime.

This is the number of indices i such that i\pi(i)-1 is prime. Note that the numbers 0 and 1 may arise, but are not prime.

References

[1] Sun, Z.-W. Primes arising from permutations MathOverflow:315259

Code

def statistic(pi): return sum(1 for i in pi if is_prime(i*pi(i) - 1))

Created

Nov 14, 2018 at 09:09 by

**Martin Rubey**Updated

May 22, 2023 at 22:55 by

**Will Dowling**
1 Comments (hide)

Martin Rubey

23 May 8:59

23 May 8:59

This is hard to read. Also, the first line should always contain a hint about which collection the statistic is in, eg. "of a permutation". Why "column"?

Identifier

St001285:
Permutations ⟶ ℤ

Values

No modified entries

Description

The number of column-sum primes.

This is the number of sums $i+\pi(i)$ that are prime.

This is the number of sums $i+\pi(i)$ that are prime.

Diff Description

The number of ~~prime~~column-sum primes.

This i~~n~~s the ~~column sums of the two line notation of a permutation~~number of sums i+\pi(i) that are prime.

This i

References

[1] Bradley, P. Prime Number Sums arXiv:1809.01012

Code

def statistic(pi): return sum(1 for i in pi if is_prime(pi(i) + i))

Created

Nov 14, 2018 at 07:25 by

**Martin Rubey**Updated

May 22, 2023 at 22:53 by

**Will Dowling**
1 Comments (hide)

Martin Rubey

23 May 8:59

23 May 8:59

This is hard to read. Also, the first line should always contain a hint about which collection the statistic is in, eg. "of a permutation". Why "column"?

23 May 8:56