A391691 Number of congruences of the lattice of alternating sign matrices of size n such that minima and maxima of congruence classes are permutations.

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

Offset

1,2

Comments

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).

Links

Table of n, a(n) for n=1..8.

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 4 p. 36.

Crossrefs

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

Sequence in context: A319285 A316652 A330471 * A121417 A232549 A369778

Adjacent sequences: A391688 A391689 A391690 * A391692 A391693 A391694

Keyword

nonn,more

Author

Ludovic Schwob, Dec 17 2025

Status

approved