Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals

Satoshi Murai

doi:10.1007/s10801-007-0095-y

Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals

Satoshi Murai^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

In this paper, we will show that the color-squarefree operation does not change the graded Betti numbers of strongly color-stable ideals. In addition, we will give an example of a nonpure balanced complex which shows that colored algebraic shifting, which was introduced by Babson and Novik, does not always preserve the dimension of reduced homology groups of balanced simplicial complexes.

Original language	English
Pages (from-to)	383-398
Number of pages	16
Journal	Journal of Algebraic Combinatorics
Volume	27
Issue number	3
DOIs	https://doi.org/10.1007/s10801-007-0095-y
Publication status	Published - 2008 May
Externally published	Yes

Keywords

Balanced complexes
Colored algebraic shifting
Graded Betti numbers

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.1007/s10801-007-0095-y

Cite this

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title = "Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals",

abstract = "In this paper, we will show that the color-squarefree operation does not change the graded Betti numbers of strongly color-stable ideals. In addition, we will give an example of a nonpure balanced complex which shows that colored algebraic shifting, which was introduced by Babson and Novik, does not always preserve the dimension of reduced homology groups of balanced simplicial complexes.",

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author = "Satoshi Murai",

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N2 - In this paper, we will show that the color-squarefree operation does not change the graded Betti numbers of strongly color-stable ideals. In addition, we will give an example of a nonpure balanced complex which shows that colored algebraic shifting, which was introduced by Babson and Novik, does not always preserve the dimension of reduced homology groups of balanced simplicial complexes.

AB - In this paper, we will show that the color-squarefree operation does not change the graded Betti numbers of strongly color-stable ideals. In addition, we will give an example of a nonpure balanced complex which shows that colored algebraic shifting, which was introduced by Babson and Novik, does not always preserve the dimension of reduced homology groups of balanced simplicial complexes.

KW - Balanced complexes

KW - Colored algebraic shifting

KW - Graded Betti numbers

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Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals

Abstract

Keywords

ASJC Scopus subject areas

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