有限域上增强主秩特征序列的组合性质

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2021-06-12 DOI:10.1515/spma-2021-0154

P. Dukes, Xavier Mart'inez-Rivera

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引用次数: 0

摘要

摘要定义对称矩阵B∈𝔽n×n的增强主秩特征序列(epr-sequence)为l_1, l_2···l_1，其中l_1∈{a, S, n}，根据B的阶j的主次幂是否全部、部分但不全部、或全部不为非零。在第二作者最近对场上对称矩阵的epr序列的分类的基础上，我们开始了对情形的研究。此外，有限域上的epr序列与Ramsey理论和编码理论有联系。

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Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields

Abstract The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽n×n is defined as ℓ1ℓ2· · · ℓn, where ℓj ∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero. Building upon the second author’s recent classification of the epr-sequences of symmetric matrices over the field 𝔽 = 𝔽2, we initiate a study of the case 𝔽= 𝔽3. Moreover, epr-sequences over finite fields are shown to have connections to Ramsey theory and coding theory.

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.