Signed excedance enumeration via determinants

被引：11
|
作者：
Sivasubramanian, Sivaramakrishnan [1 ]
机构：
[1] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India
来源：
ADVANCES IN APPLIED MATHEMATICS | 2011年 / 47卷 / 04期
关键词：
Determinant; Signed-excedance; Enumeration; EULERIAN-NUMBERS;
D O I：
10.1016/j.aam.2011.02.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show a simple connection between determinants and signed-excedance enumeration of permutations. This gives us an alternate proof of a result of Mantaci about enumerating signed excedances in permutations. The connection also gives an alternate proof of a result of Mantaci and Rakotondrajao about enumerating signed excedances over derangements. Motivated by this connection, we define several excedance-like statistics on permutations and show interesting values for their signed enumerator. In some cases, we also obtain the signed excedance-like statistic enumerator with respect to positive integral weights. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：783 / 794
页数：12
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