A Criterion of Properness for a Family of Functions

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A Criterion of Properness for a Family of Functions

Journal of Mathematical Sciences. 2024. Vol. 284. No. 4. P. 451–459.

A.V. Galatenko, Pankratiev A. E., Tsaregorodtsev K. D.

Proper families of functions are a convenient apparatus for specification of large parametric classes of quasigroups and n-quasigroups. K. D. Tsaregorodtsev noticed that in the Boolean case a family is proper if and only if every mapping specified by the family or any of its subfamilies has a unique fixed point. We extend this result to the case of k-valued logics for k > 2. We also show that reencoding transformations used in the extended criterion enriched (in terms of composition) with consistent renumbering of variables and functions form the stabilizer of the set of all proper families of the given size.

Language: English

DOI

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We consider an interesting class of combinatorial symmetries of polytopes which we call edge-length preserving combinatorial symmetries. These symmetries not only preserve the combinatorial structure of a polytope but also map each edge of the polytope to an edge of the same length. We prove a simple sucient condition for a polytope to realize all ...

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Vladimir L. Popov, / Series math "arxiv.org". 2019.

It is shown that the main result of N. R. Wallach, Principal orbit type theorems for reductive algebraic group actions and the Kempf--Ness Theorem, arXiv:1811.07195v1 (17 Nov 2018) is a special case of a more general statement, which can be deduced, using a short argument, from the classical Richardson and Luna theorems. ...

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