

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
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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 PermutationTuple 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), 45414568.
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: A209305 A182957 A307375 * 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) from Evgeny Kapun, Dec 11 2016


STATUS

approved



