Реферат: A function $f:\{0,...,q-1\}^n\to\{0,...,q-1\}$ invertible in each argument is called a latin hypercube. A collection $(\pi_0,\pi_1,...,\pi_n)$ of permutations of $\{0,...,q-1\}$ is called an autotopism of a latin hypercube $f$ if $\pi_0f(x_1,...,x_n)=f(\pi_1x_1,...,\pi_nx_n)$ for all $x_1$, ..., $x_n$. We call a latin hypercube isotopically transitive (topolinear) if its group of autotopisms acts transitively (regularly) on all $q^n$ collections of argument values. We prove that the number of nonequivalent topolinear latin hypercubes grows exponentially with respect to $\sqrt{n}$ if $q$ is even and exponentially with respect to $n^2$ if $q$ is divisible by a square. We show a connection of the class of isotopically transitive latin squares with the class of G-loops, known in noncommutative algebra, and establish the existence of a topolinear latin square that is not a group isotope. We characterize the class of isotopically transitive latin hypercubes of orders $q=4$ and $q=5$.

Библиографическая ссылка: Krotov D.S. , Potapov V.N.
Constructions of transitive latin hypercubes
European Journal of Combinatorics. 2016. V.54. P.51-64. DOI: 10.1016/j.ejc.2015.12.001 WOS Scopus РИНЦ OpenAlex

Даты:

Поступила в редакцию:	28 апр. 2015 г.
Принята к публикации:	2 дек. 2015 г.
Опубликована online:	24 дек. 2015 г.

Идентификаторы БД:

Web of science:	WOS:000371360600004
Scopus:	2-s2.0-84950998135
РИНЦ:	26801587
OpenAlex:	W2113012511

Цитирование в БД:

БД	Цитирований
Web of science	1
Scopus	2
РИНЦ	4
OpenAlex	2

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