On affine classification of permutations on the space GF(2)3
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Fedor M. Malyshev
Abstract
We give an elementary proof that by multiplication on left and right by affine permutations A, B ∈ AGL(3, 2) each permutation π : GF(2)3 → GF(2)3 may be reduced to one of the 4 permutations for which the 3 × 3-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.
Originally published in Diskretnaya Matematika (2018) 30, №3, 77–87 (in Russian).
Acknowledgment
The author is grateful to A. V. Cheremushkin for useful discussions.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Periodic properties of pushdown automata
- Burnside-type problems in discrete geometry
- On affine classification of permutations on the space GF(2)3
- Limit distributions of the maximal distance to the nearest neighbour
- Elementary transformations of systems of equations over quasigroups and generalized identities
- Asymptotics for the logarithm of the number of k-solution-free sets in Abelian groups
- On the distribution of multiple power series regularly varying at the boundary point
- A letter to the Editor
Articles in the same Issue
- Frontmatter
- Periodic properties of pushdown automata
- Burnside-type problems in discrete geometry
- On affine classification of permutations on the space GF(2)3
- Limit distributions of the maximal distance to the nearest neighbour
- Elementary transformations of systems of equations over quasigroups and generalized identities
- Asymptotics for the logarithm of the number of k-solution-free sets in Abelian groups
- On the distribution of multiple power series regularly varying at the boundary point
- A letter to the Editor
