A391692 Number of distinct sets of the form J(P_s)\J(P_t) where s > t are two permutations of size n differing by a transposition and J(M) is the set of join-irreducible elements below M in the lattice of alternating sign matrices.

0, 1, 9, 52, 260, 1291, 6915, 41814, 289758, 2291381, 20436469, 203035832, 2222932248, 26583044399, 344675421975, 4815660285162, 72118777001154, 1152405604102329, 19570137802779369, 351953247879257452, 6682192854727098972, 133560657688368845779

Offset

1,3

Comments

Sets of the form J(P_s)\J(P_t) where s covers t in the Bruhat order are counted by A034009.

Links

Table of n, a(n) for n=1..22.

Florent Hivert, Vincent Pilaud, and Ludovic Schwob, Heaps of rhombic dodecahedra, catalan congruences on alternating sign matrices, and bases of the Temperley-Lieb algebra, arXiv:2511.06968 [math.CO], 2025. See Table 3 p. 32.

Formula

G.f.: (x^2/(1-x)^4) * Sum_{a,b,c,d,e>=0} x^(a+b+c+d+e)*(a+b+c)!*(a+d+e)!/(a!*b!*c!*d!*e!).

Crossrefs

Cf. A001809 (number of edges of the Bruhat graph), A034009.

Sequence in context: A120665 A163941 A289418 * A292488 A282179 A278000

Adjacent sequences: A391689 A391690 A391691 * A391693 A391694 A391695

Keyword

nonn

Author

Ludovic Schwob, Dec 17 2025

Status

approved