群图上的芯片发射

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-06-12 DOI:10.1016/j.disc.2025.114631

Margaret Meyer, Dmitry Zakharov

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引用次数: 0

摘要

定义了有限群图的拉普拉斯矩阵和雅可比群。证明了群图的雅可比矩阵阶的矩阵树定理和类数公式的类似性质。给定作用于图X上的群G，我们定义了X的雅可比群与群X//G的商图之间的自然推回映射。对于G=Z/2Z的情况，我们还证明了前推映射核阶的一个组合公式。

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Chip-firing on graphs of groups

We define the Laplacian matrix and the Jacobian group of a finite graph of groups. We prove analogues of the matrix tree theorem and the class number formula for the order of the Jacobian of a graph of groups. Given a group G acting on a graph X, we define natural pushforward and pullback maps between the Jacobian groups of X and the quotient graph of groups

X / / G

. For the case

G = Z / 2 Z

, we also prove a combinatorial formula for the order of the kernel of the pushforward map.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.