A371505 Number of sub-monoids of the monoid of uniform block permutations of size n that contain the symmetric group S_n.

1, 2, 3, 6, 10, 31, 63, 287, 1099, 8640, 62658, 1546891, 29789119, 2525655957

Offset: 1

Author

Mike Zabrocki, Apr 17 2024

Keywords

• nonn
• more

Comments

Also equal to the number of anti-chains in the poset of integer partitions of k not equal to (1^k) where mu < lambda iff mu is coarser than lambda and r(mu) >= r(lambda) where r(lambda) = smallest part of lambda not equal to 1.

Examples

			a(3) = 3 because the uniform block permutations of size 3; S_3; and the monoid consisting of S_3 and the element with one block are the only three sub-monoids.
		

Links

• D. G. FitzGerald, A presentation for the monoid of uniform block permutations, Bulletin of the Australian Mathematical Society, 68(2) (2003), 317--324.
• Rosa Orellana, Franco Saliola, Anne Schilling, and Mike Zabrocki, Plethysm and the algebra of uniform block permutations, Alg. Comb., Volume 5, no. 5 (2022), pp. 1165--1203.
• Rosa Orellana, Franco Saliola, Anne Schilling, and Mike Zabrocki, The lattice of submonoids of the uniform block permutations containing the symmetric group, arXiv:2405.09710 [math.CO], 2024. See p. 3.