论拉普拉斯学派与单纯复合体的失向性

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2025-07-09 DOI:10.1007/s00013-025-02146-6

R. Balaji, Gargi Lather, Vinayak Gupta

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引用次数: 0

摘要

设K是一个n维的简单复形。我们研究了K的上拉普拉斯矩阵的谱。设L为\((N-1)\) K的上拉普拉斯矩阵。我们证明了当且仅当K不可定向时，L和|的最大特征值L|相等。我们也推导出L的前k个最大特征值和的下界。

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On Laplacians and the disorientability of a simplicial complex

Let K be an N-dimensional simplicial complex. We investigate the spectrum of the up Laplacian matrix of K. Let L be the \((N-1)\)th up Laplacian matrix of K. We show that the largest eigenvalues of L and |L| are equal if and only if K is disorientable. We also derive lower bounds for the sum of the first k largest eigenvalues of L.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.