A290138 Number of maximal subgroups of the symmetric group S_n.

0, 1, 4, 8, 22, 53, 184, 353, 1376, 3977, 363904, 396498, 39920896, 40060127, 1543910, 4687418, 1307674433536, 1307902407753, 355687428358144, 355691118382364, 162615882312376736, 1267150213999727, 51090942171713634304, 51090956256672365547

Offset: 1

Author

James Mitchell and Wilf A. Wilson, Jul 21 2017

Keywords

• nonn

Comments

a(n) + 1, n > 1, is the number of maximal subsemigroups of each of the following monoids of degree n: the full transformation monoid, the symmetric inverse monoid, the dual symmetric inverse monoid, the uniform block bijection monoid, and the Brauer monoid.

a(n) + 2 is the number of maximal subsemigroups of the partial transformation monoid of degree n.

a(n) + 3, n > 1, is the number of maximal subsemigroups of the partial Brauer monoid of degree n.

a(n) + 4, n > 1, is the number of maximal subsemigroups of the partition monoid of degree n.

Links

• Wilf A. Wilson, Table of n, a(n) for n = 1..84
• Utsithon Chaichompoo and Kritsada Sangkhanan, Transformation Semigroups Which Are Disjoint Union of Symmetric Groups, arXiv:2411.15081 [math.RA], 2024. See p. 10.
• James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017.

Crossrefs

Cf. A066115.

Programs

GAP

Sum(List(ConjugacyClassesMaximalSubgroups(SymmetricGroup(n)), Size));