作为条件独立性模型的矩阵和定向矩阵的公理化

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-05-17 DOI:10.1137/23m1558653

Xiangying Chen

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引用次数: 0

摘要

SIAM 离散数学杂志》第 38 卷第 2 期第 1526-1536 页，2024 年 6 月。摘要矩阵（Matroids）和半矩阵（semigraphoids）是离散结构，分别抽象和概括了向量间的线性独立性和随机变量间的条件独立性。尽管条件独立性与线性独立性的性质不同，但这两个领域之间存在着深刻的联系，目前仍在积极研究之中。本文给出了将矩阵嵌入条件独立性结构及其定向对应结构的表征，从而引出了矩阵和定向矩阵的新公理系统。

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An Axiomatization of Matroids and Oriented Matroids as Conditional Independence Models

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1526-1536, June 2024.
Abstract. Matroids and semigraphoids are discrete structures abstracting and generalizing linear independence among vectors and conditional independence among random variables, respectively. Despite the different nature of conditional independence from linear independence, deep connections between these two areas are found and are still undergoing active research. In this paper, we give a characterization of the embedding of matroids into conditional independence structures and its oriented counterpart, which leads to new axiom systems of matroids and oriented matroids.

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.