On the number of n-ary quasigroups of finite order Full article
| Journal |
Discrete Mathematics and Applications
ISSN: 0924-9265 , E-ISSN: 1569-3929 |
||
|---|---|---|---|
| Output data | Year: 2011, Volume: 21, Number: 5-6, Pages: 575-585 Pages count : 11 DOI: 10.1515/dma.2011.035 | ||
| Authors |
|
||
| Affiliations |
|
Abstract:
Let $Q(n,k)$ be the number of $n$-ary quasigroups of order $k$. We derive a recurrent formula for $Q(n,k)$. We prove that for all $n≥2$ and $k≥5$ the following inequalities hold:
$$ ((k−3)/2)^{n/2}((k−1)/2)^{n/2} < log_2 Q(n,k) ≤ c_k(k−2)^n, $$
where $c_k$ does not depend on $n$. So, the upper asymptotic bound for $Q(n,k)$ is improved for any $k≥5$ and the lower bound is improved for odd $k≥7$.
Cite:
Potapov V.N.
, Krotov D.S.
On the number of n-ary quasigroups of finite order
Discrete Mathematics and Applications. 2011. V.21. N5-6. P.575-585. DOI: 10.1515/dma.2011.035 WOS Scopus РИНЦ OpenAlex
On the number of n-ary quasigroups of finite order
Discrete Mathematics and Applications. 2011. V.21. N5-6. P.575-585. DOI: 10.1515/dma.2011.035 WOS Scopus РИНЦ OpenAlex
Original:
Потапов В.Н.
, Кротов Д.С.
О числе n-арных квазигрупп конечного порядка
Дискретная математика. 2012. Т.24. №1. С.60-69. DOI: 10.4213/dm1172 РИНЦ OpenAlex
О числе n-арных квазигрупп конечного порядка
Дискретная математика. 2012. Т.24. №1. С.60-69. DOI: 10.4213/dm1172 РИНЦ OpenAlex
Dates:
| Submitted: | Dec 2, 2009 |
Identifiers:
| Web of science: | WOS:000218060300004 |
| Scopus: | 2-s2.0-84996538446 |
| Elibrary: | 28262303 |
| OpenAlex: | W2963258276 |