Unmixed and sequentially Cohen-Macaulay skew tableau ideals
Do Trong Hoang, Thanh Vu
TL;DR
This paper classifies skew tableau ideals based on their algebraic properties, specifically focusing on unmixed and sequentially Cohen-Macaulay cases, and extends these classifications to Cohen-Macaulay, Buchsbaum, and generalized Cohen-Macaulay ideals.
Contribution
It provides a complete classification of skew tableau ideals with certain algebraic properties, a novel contribution in combinatorial commutative algebra.
Findings
Classified all unmixed skew tableau ideals.
Classified all sequentially Cohen-Macaulay skew tableau ideals.
Extended classifications to Cohen-Macaulay, Buchsbaum, and generalized Cohen-Macaulay skew tableau ideals.
Abstract
We associate a {\it skew tableau ideal} to each filling of a skew Ferrers diagram with positive integers. We classify all unmixed and sequentially Cohen-Macaulay skew tableau ideals. Consequently, we classify all Cohen-Macaulay, Buchsbaum, and generalized Cohen-Macaulay skew tableau ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Neurological Disorders and Treatments