OFFSET
1,3
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.
PROG
(GAP) Sum(List(ConjugacyClassesMaximalSubgroups(SymmetricGroup(n)), Size));
CROSSREFS
KEYWORD
nonn
AUTHOR
James Mitchell and Wilf A. Wilson, Jul 21 2017
STATUS
approved