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Diskretnaya Matematika, 2018, Volume 30, Issue 3, Pages 77–87
DOI: https://doi.org/10.4213/dm1495 (Mi dm1495) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

F. M. Malyshev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/dm1495
Abstract: We give an elementary proof that by multiplication on left and right by affine permutations $A,B\in AGL(3,2)$ each permutation $\pi:GF(2)^3\rightarrow GF(2)^3$ may be reduced to one of the 4 permutations for which the $3\times3$-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 Pólya enumerative theory.
Keywords: permutation, affine transformation, Pólya theory, de Brouijn's theorem.
Received: 09.01.2018
English version:
Discrete Mathematics and Applications, 2019, Volume 29, Issue 6, Pages 363–371
DOI: https://doi.org/10.1515/dma-2019-0035
Bibliographic databases:
Document Type: Article
UDC: 512.542.74
Language: Russian
Citation: F. M. Malyshev, “On affine classification of permutations on the space $GF(2)^3$”, Diskr. Mat., 30:3 (2018), 77–87; Discrete Math. Appl., 29:6 (2019), 363–371
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Дискретная математика
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