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A007767 Number of pairs of permutations of degree n that avoid (12,21). 2
1, 1, 3, 17, 151, 1899, 31711, 672697, 17551323, 549500451, 20246665349, 864261579999, 42190730051687, 2329965898878307 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A pair of permutations (p,q) of degree n avoid (12,21) if there do not exist indices 1<=i<j<=n such that p_i < p_j and q_j < q_i. - Noam Zeilberger, Jun 06 2016 (via Steve Linton)

Number of intervals (i.e. ordered pairs (x,y) such that x<=y) in the permutation lattice of size n, that is, pairs of permutations (x,y) related by the weak Bruhat order x<=y iff inversions(x) is a subset of inversions(y) (see Hammett and Pittel, p. 4567). - Noam Zeilberger, Jun 01 2016

LINKS

Table of n, a(n) for n=0..13.

Grégory Chatel, Vincent Pilaud, Viviane Pons, The weak order on integer posets, arXiv:1701.07995 [math.CO], 2017.

Joël Gay, Vincent Pilaud, The weak order on Weyl posets, arXiv:1804.06572 [math.CO], 2018.

Benjamin Gunby, Asymptotics of Pattern Avoidance in the Permutation-Tuple and Klazar Set Partition Settings, arXiv:1609.06023 [math.CO], 2017.

Adam Hammett and Boris Pittel, How often are two permutations comparable?, Transactions of the AMS 360:9 (2008), 4541-4568.

Evgeny Kapun, Java program for generating terms a(0)-a(13).

FORMULA

a(n) = Sum_{k=1..n!} k * A263754(n,k). - Alois P. Heinz, Jun 06 2016

PROG

(Java) See link.

CROSSREFS

Cf. A000260, A263754.

Sequence in context: A303063 A209305 A182957 * A075820 A145081 A020562

Adjacent sequences:  A007764 A007765 A007766 * A007768 A007769 A007770

KEYWORD

nonn,more

AUTHOR

Steve Linton

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Jun 06 2016

a(10)-a(13) by Evgeny Kapun, Dec 11 2016

STATUS

approved

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Last modified August 20 20:33 EDT 2018. Contains 313927 sequences. (Running on oeis4.)