The Largest Subsemilattices of the Semigroup of Transformations on a Finite Set
Araújo, João · Konieczny, Janusz
Original · EN
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 2ⁿ⁻¹ elements and that there are precisely n subsemilattices of size exactly 2ⁿ⁻¹, each isomorphic to the semilattice of idempotents of the symmetric inverse semigroup on a set with n-1 elements.
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