On reducibility of n-ary quasigroups
| dc.creator | Krotov, Denis | |
| dc.date | 2006-07-12 | |
| dc.date | 2007-07-17 | |
| dc.date.accessioned | 2026-07-07T10:09:14Z | |
| dc.date.available | 2026-07-07T10:09:14Z | |
| dc.description | An $n$-ary operation $Q:S^n -> S$ is called an $n$-ary quasigroup of order $|S|$ if in the equation $x_{0}=Q(x_1,...,x_n)$ knowledge of any $n$ elements of $x_0$, ..., $x_n$ uniquely specifies the remaining one. $Q$ is permutably reducible if $Q(x_1,...,x_n)=P(R(x_{s(1)},...,x_{s(k)}),x_{s(k+1)},...,x_{s(n)})$ where $P$ and $R$ are $(n-k+1)$-ary and $k$-ary quasigroups, $s$ is a permutation, and $1<k<n$. An $m$-ary quasigroup $S$ is called a retract of $Q$ if it can be obtained from $Q$ or one of its inverses by fixing $n-m>0$ arguments. We prove that if the maximum arity of a permutably irreducible retract of an $n$-ary quasigroup $Q$ belongs to $\{3,...,n-3\}$, then $Q$ is permutably reducible. Keywords: n-ary quasigroups, retracts, reducibility, distance 2 MDS codes, latin hypercubes | |
| dc.description | 13 pages; presented at ACCT'2004 v2: revised; bibliography updated; 2 appendixes | |
| dc.identifier | https://arxiv.org/abs/math/0607284 | |
| dc.identifier | http://arxiv.org/abs/math/0607284 | |
| dc.identifier | Discrete Math. 308(22) 2008, 5289-5297 | |
| dc.identifier | doi:10.1016/j.disc.2007.08.099 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171256 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 05B99 (Primary); 20N15, 94B25 (Secondary) | |
| dc.title | On reducibility of n-ary quasigroups | |
| dc.type | text |