Toric rings of nonsimple polyominoes
| Autor: | Akihiro Shikama |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Class (set theory)
Ideal (set theory) Mathematics::Combinatorics Polyomino Mathematics::Commutative Algebra Plane (geometry) Computer Science::Computational Geometry Commutative Algebra (math.AC) Mathematics - Commutative Algebra Combinatorics Matrix (mathematics) Computer Science::Discrete Mathematics FOS: Mathematics Commutative algebra Mathematics::Symplectic Geometry Mathematics |
| Popis: | IntroductionPolyominoes are two dimensional objects which are originally rooted in recre-ational mathematics and combinatorics. They have been widely discussed in con-nection with tiling problems of the plane. Typically, a polyomino is plane figureobtained by joining squares of equal sizes, which are known as cells. In connectionwith commutative algebra, polyominoes are first discussed in [5] by assigning eachpolyomino the ideal of inner 2-minors or the polyominoideal. The study of ideal oft-minors of an m×n matrix is a classical subject in commutative algebra. The classof polyomino ideal widely generalizes the class of ideals of 2-minors of m×n matrixas well ass the ideal of inner 2-minors attached to a two sided ladder.Let P be a polyomino and K be a field. We denote by I |
| Databáze: | OpenAIRE |
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