Toric representations of algebras defined by certain nonsimple polyominoes

TL;DR

This paper presents a toric representation of the algebraic structure associated with polyominoes formed by removing convex shapes from rectangles, advancing the understanding of their algebraic properties.

Contribution

It introduces a novel toric representation for the algebra of polyominoes created by excising convex polyominoes from rectangles, expanding algebraic insights into these geometric objects.

Findings

Provides a toric model for the algebra of certain polyominoes

Connects geometric removal of convex shapes to algebraic structures

Enhances understanding of polyomino algebraic properties

Abstract

In this paper we give a toric representation of the associated ring of a polyomino which is obtained by removing a convex polyomino from its ambient rectangle.