On affine classification of permutations on the space GF(2)3

被引：1
|
作者：
Malyshev, Fedor M. [1 ]
机构：
[1] Russian Acad Sci, Steklov Math Inst, Moscow, Russia
来源：
DISCRETE MATHEMATICS AND APPLICATIONS | 2019年 / 29卷 / 06期
关键词：
permutation; affine transformation; Polya theory; de Brouijn's theorem;
D O I：
10.1515/dma-2019-0035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give an elementary proof that by multiplication on left and right by affine permutations A, B is an element of AGL(3, 2) each permutation pi:GF(2)(3)-> GF(2)(3) may be reduced to one of the 4 permutations for which the 3x3-matrices consisting of the coefficients of quadratic terms of coordinate functions have as an invariant the rank, which is either 3, or 2, or 1, or 0, respectively. For comparison, we evaluate the number of classes of affine equivalence by the Polya enumerative theory.
引用
收藏
页码：363 / 371
页数：9
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