Toric rings of nonsimple polyominoes
Akihiro Shikama
TL;DR
This paper investigates the algebraic structure of toric rings associated with nonsimple polyominoes, specifically those formed by subtracting one rectangle from another, expanding understanding beyond simple polyominoes.
Contribution
It identifies the toric ring structure for a new class of nonsimple polyominoes, namely rectangles minus rectangles, extending previous results on simple polyominoes.
Findings
Toric rings of rectangle minus rectangle polyominoes are characterized.
Extension of toric ring theory from simple to certain nonsimple polyominoes.
New algebraic properties identified for these nonsimple polyominoes.
Abstract
It is known that toric ring of a simple polyomino is ring homomorphic to a edge ring of a weakly chordal bipartite graph. In this paper we identify the toric ring of nonsimple polyominoes which are of the form "rectangle minus rectangle".
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Cholinesterase and Neurodegenerative Diseases