Tropical Roots and Their Multiplicities on the Subsemigroup of Order-Decreasing and Order-Preserving Full Transformation

Abstract

Let be ordered finite set. The tropical geometry was utilized to analyze the subsemigroup of order-decreasing and order-preserving semigroups, denoted as full transformation . The elements of classical algebra within were transformed into tropical polynomials, allowing for the determination of tropical roots and their multiplicities through the tropical curve, which was visualized using GeoGebra.