奇、偶双随机矩阵及其积和式的若干注记  

Some Notes on Odd and Even Doubly-stochastic Matrices,and their Permanents

作　　者：黄宇飞[1] 

机构地区：[1]广州民航职业技术学院,广东广州510403

出　　处：《新疆师范大学学报（自然科学版）》2014年第4期49-52,共4页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：国家自然科学基金数学天元基金资助项目(No.11326221)资助

摘　　要：文章主要研究了奇、偶双随机矩阵及其(奇、偶)积和式的有关问题。一方面,通过分析双随机矩阵的奇偶性,说明了刻画奇双随机矩阵和偶双随机矩阵的等价性;另一方面,参照双随机矩阵其积和式的下确界问题(即著名的Van der WaerdenEgorychev-Falikman定理),对奇、偶双随机矩阵其(奇、偶)积和式的确界问题分别进行了探讨。This paper mainly studies odd and even doubly-stochastic matrices,and the （ odd and even） per-manents of them, respectively. On one hand, by analyzing the parity of doubly-stochastic matrices, we illustrate the equivalence of characterizing the odd and even doubly-stochastic matrices. On the other hand, with reference to the best lower bound for the permanents of doubly-stochastic matrices （ that is, the famous Van der Waerden-Ego-rychev-Falikman theorem） , we discuss the best bound problems for the （ odd and even） permanents of odd and e？ven doubly-stochastic matrices, respectively.

关 键 词：奇双随机矩阵 偶双随机矩阵 奇积和式 偶积和式 

分 类 号：O151.21[理学—数学]