Gr\"obner bases of balanced polyominoes
J\"urgen Herzog, Ayesha Asloob Qureshi, Akihiro Shikama
TL;DR
This paper introduces balanced polyominoes, proving their associated ideals are prime and have quadratic Gr"obner bases, and shows that certain classes of polyominoes are simple and balanced.
Contribution
It defines balanced polyominoes and establishes their algebraic properties, including primality and quadratic Gr"obner bases, expanding understanding of polyomino ideal structures.
Findings
Balanced polyominoes have prime ideals.
Their ideals admit quadratic Gr"obner bases.
Row/column convex and tree-like polyominoes are simple and balanced.
Abstract
We introduce balanced polyominoes and show that their ideal of inner minors is a prime ideal and has a quadratic Gr\"obner basis with respect to any monomial order, and we show that any row or column convex and any tree-like polyomino is simple and balanced.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory