Wei-type duality theorems for matroids

被引：0
|
作者：
Thomas Britz
Trygve Johnsen
Dillon Mayhew
Keisuke Shiromoto
机构：
[1] University of New South Wales,School of Mathematics and Statistics
[2] University of Tromsø,Department of Mathematics and Statistics
[3] Statistics and Operations Research,School of Mathematics
[4] Victoria University,Department of Mathematics and Engineering
[5] Kumamoto University,undefined
来源：
Designs, Codes and Cryptography | 2012年 / 62卷
关键词：
Matroid duality theorems; Demi-matroid; Poset code; Wei’s Duality Theorem; Matroid design; 05B35; 06A07; 94B05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present several fundamental duality theorems for matroids and more general combinatorial structures. As a special case, these results show that the maximal cardinalities of fixed-ranked sets of a matroid determine the corresponding maximal cardinalities of the dual matroid. Our main results are applied to perfect matroid designs, graphs, transversals, and linear codes over division rings, in each case yielding a duality theorem for the respective class of objects.
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收藏
页码：331 / 341
页数：10
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