准晶体图的局部刻划

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2025-05-15 DOI:10.1016/j.ejc.2025.104172

Alan J. Cain , António Malheiro , Fátima Rodrigues , Inês Rodrigues

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引用次数: 0

摘要

通过提出一组局部公理，给出了An−1型准晶图的局部表征，这些公理类似于Stembridge为简单系根晶体图引入的公理，但仅限于An−1型。还证明了满足这些公理的准晶体图在Cain， Guilherme和Malheiro最近引入的张量积下是封闭的。推导出该图的每个连通分量都有唯一的最高权元，其权元是一个组合，该图同构于半标准准带状表的准晶体图。

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A local characterization of quasi-crystal graphs

A local characterization of quasi-crystal graphs of type

A_{n - 1}

is provided, by presenting a set of local axioms, similar to the ones introduced by Stembridge for crystal graphs of simply-laced root systems, but restricted to type

A_{n - 1}

. It is also shown that quasi-crystal graphs satisfying these axioms are closed under the tensor product recently introduced by Cain, Guilherme and Malheiro. It is deduced that each connected component of such a graph has a unique highest weight element, whose weight is a composition, and it is isomorphic to a quasi-crystal graph of semistandard quasi-ribbon tableaux.

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.