未混合和Cohen-Macaulay加权定向Kőnig图

IF 0.4 4区数学 Q4 MATHEMATICS

Studia Scientiarum Mathematicarum Hungarica Pub Date : 2019-09-29 DOI:10.1556/012.2021.58.3.1499

Yuriko Pitones, E. Reyes, R. Villarreal

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引用次数: 9

摘要

设D为一个加权有向图，其底层图为G，设I (D)为其边理想。如果G没有3、5或7环，或者G为Kőnig，我们在I (D)未混合时进行表征。如果G没有3环或5环，或者G为Kőnig，我们在I (D)为Cohen-Macaulay时进行表征。证明当且仅当当G的周长大于7或G为Kőnig且不存在4环时，I (D)是Cohen-Macaulay时，I (D)是不混合的。

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Unmixed and Cohen–Macaulay Weighted Oriented Kőnig Graphs

Let D be a weighted oriented graph, whose underlying graph is G, and let I (D) be its edge ideal. If G has no 3-, 5-, or 7-cycles, or G is Kőnig, we characterize when I (D) is unmixed. If G has no 3- or 5-cycles, or G is Kőnig, we characterize when I (D) is Cohen–Macaulay. We prove that I (D) is unmixed if and only if I (D) is Cohen–Macaulay when G has girth greater than 7 or G is Kőnig and has no 4-cycles.

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来源期刊

Studia Scientiarum Mathematicarum Hungarica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.