TROPICAL GEOMETRIC APPROACH TO SIGNED FULL TRANSFORMATION SEMIGROUPS

Abstract

Let Ω𝑘={1,2,3,−−,𝑘} be a finite set and 𝑆𝑇𝑘 be the signed full transformation semigroups. This work surveys the connection between tropical geometry and semigroup theory. Tropical geometry were applied on 𝑆𝑇𝑘 by degenerating elements from classical into tropical algebra. Through this approach, we analyze the structure of these transformations and determine the heights of their multiplicities through tropical curves. This study provides new perceptions into the algebraic properties of 𝑆𝑇𝑘.