5 papers
New Quantitative Bounds for the -Theorem for Unions of Convex Sets
Chaya Keller, Shakhar Smorodinsky
A set in is -convex if it is the union of at most convex sets. A family satisfies the property if among any sets in , some intersect. L…
Simplicity of Augmentation Submodules in Monoids with 0-Minimal Ideals of Rank Greater than Two
M. H. Shahzamanian
In this paper, we construct explicit families of transformation monoids whose augmentation submodules are simple and whose associated 0-minimal J-classes have rank greater than two…
The determinant of \(\lll\)-smooth semigroups
M. H. Shahzamanian
This paper continues the investigation of non-zero determinants associated with finite semigroups containing a pair of non-commuting idempotents, as initiated in~\cite{Sha-Det2}. W…
The Layered Catalan Monoids: Structure and Determinants
M. H. Shahzamanian
In this paper, we introduce and study a class of monoids, called Layered Catalan Monoids (\( {LC}_n \)), which satisfy the structural conditions for -smoothness as defined in~…
A step to compute the determinant of finite semigroups not in ECom
M. H. Shahzamanian
The purpose of this paper is to begin studying the computation of the nonzero determinant of semigroups within the class of finite semigroups that possesses a pair of non-commutati…