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数学进展 - 2016, Vol. 45(2): 161-175
综述文章
组合矩阵的结构指数 ------组合矩阵指数的系统化
Structural Indices of Combinatorial Matrix------ The Systematization of Combinatorial Matrix Indices

黄宇飞1,柳柏濂2
HUANG Yufei1, LIU Bolian2

1. 广州民航职业技术学院, 广州,广东, 510403;
2. 华南师范大学数学科学学院, 广州, 广东, 510631
1. Guangzhou Civil Aviation College, Guangzhou, Guangdong,510403, P. R. China;
2. College of Mathematical Science, South China Normal University, Guangzhou, Guangdong, 510631, P. R. China

收稿日期: 2014-05-13
出版日期: 2016-03-10
2016, Vol. 45(2): 161-175
DOI: 10.11845/sxjz.2014006a


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摘要 组合矩阵的指数理论是组合矩阵论中核心的研究内容,其不仅具有重要的理论价值,而且在计算机科学、遍历理论、通讯理论、社会学和经济学中都有广泛的应用.本文将综述若干经典的组合矩阵指数,并采用统一的观点,把组合矩阵的各类指数归结为``组合矩阵的结构指数"这一理论体系,开拓了组合矩阵指数理论研究的新视野.
Abstract:The index theory of combinatorial matrix is the central research of combinatorial matrix theory.Combinatorial matrix index theory not only has important theoretical value,but also has a wide range of practical applications in many aspects, e.g., computer science, ergodic theory, communications theory, sociology and economics.In this paper, we summarize a number of classic indices of combinatorial matrix,and adopt a unified view to sum them up as structural indices of combinatorial matrix.This theoretical system opens up a new field for the research of index theory.
PACS:  O151.21  
基金资助:国家自然科学基金青年科学基金(No. 11501139)和数学天元基金(No. 11326221).
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