Counting nilpotent endomorphisms

被引：12
|
作者：
Crabb, MC [1 ]
机构：
[1] Univ Aberdeen, Dept Math Sci, Aberdeen AB24 3UE, Scotland
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2006年 / 12卷 / 01期
关键词：
nilpotent matrix; Prufer code;
D O I：
10.1016/j.ffa.2005.03.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A variant of Priffer's classical proof of Cayley's theorem on the enumeration of labelled trees counts the nilpotent self-maps of a pointed finite set. Essentially, the same argument can be used to establish the result of Fine and Herstein [Illinois J. Math. 2 (1958) 499-504] that the number of nilpotent n x n matrices over the finite field F-q is q(n)((n-1)). (c) 2005 Elsevier Inc. All rights reserved.
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页码：151 / 154
页数：4
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