Let is an arbitrary partition. Again we use representation theory to find the minimum number
of elements needed to generate the wreath product of finitely many symmetric groups, and …

The rank of a semigroup is the cardinality of a smallest generating set. In this paper we
compute the rank of the endomorphism monoid of a non-trivial uniform partition of a finite …

The variant of a semigroup S with respect to an element a∈ S, denoted S a, is the
semigroup with underlying set S and operation⋆ defined by x⋆ y= xay for x, y∈ S. In this …

Let 𝒫X and 𝒮X be the partition monoid and symmetric group on an infinite set X. We show
that 𝒫X may be generated by 𝒮X together with two (but no fewer) additional partitions, and …

Based on an idea of Y. Péresse and some results of Maltcev, Mitchell and Ruškuc, we
present sufficient conditions under which the endomorphism monoid of a countably infinite …

GENERATING SETS OF SEMIGROUPS OF PARTIAL TRANSFORMATIONS PRESERVING
A ZIG-ZAG ORDER ON N Ilinka Dimitrova1, Jörg Koppitz2, Ladd Page 1 International …

The relative ranks of the monoid of endomorphisms of a strong independence algebra of
infinite rank modulo two distinguished subsets are calculated. These subsets are the group …

Semigroups of order-preserving transformations have been extensively studied for finite
chains. We study the monoid OPN of all order-preserving partial transformations on the set N …

For a group G acting on a set X, let End G (X) be the monoid of all G-equivariant
transformations, or G-endomorphisms, of X, and let Aut G (X) be its group of units. After …

The purpose of this paper is to advance our knowledge of two of the most classic and
popular topics in transformation semigroups: automorphisms and the size of minimal …