单循环多图SSC的代数表征

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2023-06-01 DOI:10.1142/s1005386723000275

Imran Ahmed, Shahid Muhmood

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引用次数: 0

摘要

我们首先介绍了多图的生成简单复形(SSC)[公式:见文]，它给出了与简单图相关的SSC的推广[公式:见文]。讨论了单循环多图族[公式:见文]的SSC的组合性质，其中[公式:见文]边包括[公式:见文]长度周期内外的多个边[公式:见文]，然后将其用于计算SSC[公式:见文]的[公式:见文]-向量和面环[公式:见文]的希尔伯特级数[公式:见文]。此外，我们找到了面理想的相关素数[公式:见文本]。最后，我们给出了[公式:见文]的同调群的一个公式，并证明了单循环多图族的SSC是Cohen-Macaulay的。

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Algebraic Characterization of SSC of Uni-Cyclic Multigraphs

We introduce first the spanning simplicial complex (SSC) of a multigraph [Formula: see text], which gives a generalization of the SSC associated with a simple graph [Formula: see text]. Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs [Formula: see text] with [Formula: see text] edges including [Formula: see text] multiple edges within and outside the cycle of length [Formula: see text], which are then used to compute the [Formula: see text]-vector and Hilbert series of face ring [Formula: see text] for the SSC[Formula: see text]. Moreover, we find the associated primes of the facet ideal [Formula: see text]. Finally, we device a formula for homology groups of [Formula: see text] and prove that the SSC of a family of uni-cyclic multigraphs is Cohen-Macaulay.

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.