The Largest Subsemilattices of the Semigroup of Transformations on a Finite Set

2010/07/27 by Araújo, João, Konieczny, Janusz
#20M20 (Primary) 06A12 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1007.4845

Abstract

Let T(X) be the semigroup of full transformations on a finite set X with n elements. We prove that every subsemilattice of T(X) has at most 2^n-1 elements and that there are precisely n subsemilattices of size exactly 2^n-1, each isomorphic to the semilattice of idempotents of the symmetric inverse semigroup on a set with n-1 elements.

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