A391691 - OEIS

A391691

Number of congruences of the lattice of alternating sign matrices of size n such that minima and maxima of congruence classes are permutations.

%I #6 Dec 23 2025 14:11:16

%S 1,2,9,69,716,8986,128065,2043636

%N Number of congruences of the lattice of alternating sign matrices of size n such that minima and maxima of congruence classes are permutations.

%C Congruences of ASM_n such that minima and maxima of congruence classes are permutations are in bijection with vertex covers of a graph on the join-irreducible elements of ASM_n (see reference).

%H Florent Hivert, Vincent Pilaud, and Ludovic Schwob, <a href="https://arxiv.org/abs/2511.06968">Heaps of rhombic dodecahedra, catalan congruences on alternating sign matrices, and bases of the Temperley-Lieb algebra</a>, arXiv:2511.06968 [math.CO], 2025. See Table 4 p. 36.

%Y Cf. A005130 (number of ASMs), A125791 (number of congruences of ASM_n), A391690.

%K nonn,more

%O 1,2

%A _Ludovic Schwob_, Dec 17 2025