22 citations · 51 across the 7 of their papers we have counts for
5 papers · 1 filter
On the reconstruction of -quasigroups of order and upper bounds on their number
Denis S. Krotov, Vladimir N. Potapov
(This is a reprint of the thesis published in the Transactions of the Conference Devoted to the 90th Anniversary Of Alexei A. Lyapunov, Novosibirsk, October 8-12, 2001, pages 323-3…
Singleton mesh patterns in multidimensional permutations
Sergey Avgustinovich, Sergey Kitaev, Jeffrey Liese +2
This paper introduces the notion of mesh patterns in multidimensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional me…
On the number of n-ary quasigroups of finite order
Denis Krotov, Vladimir Potapov
Let be the number of -ary quasigroups of order . We derive a recurrent formula for Q(n,4). We prove that for all and the following inequalities h…
On reconstructing reducible n-ary quasigroups and switching subquasigroups
Denis Krotov, Vladimir Potapov, Polina Sokolova
(1) We prove that, provided n>=4, a permutably reducible n-ary quasigroup is uniquely specified by its values on the n-ples containing zero. (2) We observe that for each n,k>=2 and…
Asymptotics for the number of n-quasigroups of order 4
Vladimir Potapov, Denis Krotov
The asymptotic form of the number of n-quasigroups of order 4 is . Keywords: n-quasigroups, MDS codes, decomposability, reducibility.