| 奇、偶双随机矩阵及其积和式的若干注记 |
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| 引用本文： | 黄宇飞.奇、偶双随机矩阵及其积和式的若干注记[J].新疆师范大学学报(自然科学版),2014(4):49-52. |
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| 作者姓名： | 黄宇飞 |
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| 作者单位： | 广州民航职业技术学院，广东 广州，510403 |
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| 基金项目： | 国家自然科学基金数学天元基金资助项目( No．11326221)资助。 |
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| 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 Waerden－Egorychev－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。
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| 关 键 词： | 奇双随机矩阵 偶双随机矩阵 奇积和式 偶积和式 |
Some Notes on Odd and Even Doubly-stochastic Matrices,and their Permanents |
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| HANG YU-fei.Some Notes on Odd and Even Doubly-stochastic Matrices,and their Permanents[J].Journal of Xinjiang Normal University(Natural Sciences Edition),2014(4):49-52. |
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| Authors: | HANG YU-fei |
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| Institution: | HANG YU-fei(Guangzhou Civil Aviation College, Guangzhou, GuangDong, 510403, China) |
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| Abstract: | 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. |
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| Keywords: | Odd doubly-stochastic matrix Even doubly-stochastic matrix Odd permanent Even permanent |
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