Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams

Kuei Nuan Lin; Yi Huang Shen

doi:10.1007/s10801-023-01217-7

Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams

Kuei Nuan Lin
, Yi Huang Shen

Penn State Greater Allegheny

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We investigate the Castelnuovo–Mumford regularity and the multiplicity of the toric ring associated with a three-dimensional Ferrers diagram. In particular, in the rectangular case, we provide direct formulas for these two important invariants. Then, we compare these invariants for an accompanying pair of Ferrers diagrams under some mild conditions and bound the Castelnuovo–Mumford regularity for more general cases.

Original language	English (US)
Pages (from-to)	1073-1101
Number of pages	29
Journal	Journal of Algebraic Combinatorics
Volume	57
Issue number	4
DOIs	https://doi.org/10.1007/s10801-023-01217-7
State	Published - Jun 2023

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.1007/s10801-023-01217-7

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abstract = "We investigate the Castelnuovo–Mumford regularity and the multiplicity of the toric ring associated with a three-dimensional Ferrers diagram. In particular, in the rectangular case, we provide direct formulas for these two important invariants. Then, we compare these invariants for an accompanying pair of Ferrers diagrams under some mild conditions and bound the Castelnuovo–Mumford regularity for more general cases.",

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AB - We investigate the Castelnuovo–Mumford regularity and the multiplicity of the toric ring associated with a three-dimensional Ferrers diagram. In particular, in the rectangular case, we provide direct formulas for these two important invariants. Then, we compare these invariants for an accompanying pair of Ferrers diagrams under some mild conditions and bound the Castelnuovo–Mumford regularity for more general cases.

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Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams

Abstract

All Science Journal Classification (ASJC) codes

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