Asymptotics for the number of n-quasigroups of order 4

The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1} 2^{2^n +1} (1+o(1))$. Keywords: n-quasigroups, MDS codes, decomposability, reducibility.Comment: 15 p., 3 fi

On the number of n-ary quasigroups of finite order

Let $Q(n,k)$ be the number of $n$-ary quasigroups of order $k$. We derive a recurrent formula for Q(n,4). We prove that for all $n\geq 2$ and $k\geq 5$ the following inequalities hold: $({k-3}/2)^{n/2}(\frac{k-1}2)^{n/2} < log_2 Q(n,k) \leq {c_k(k-2)^{n}}$, where $c_k$ does not depend on $n$. So, the upper asymptotic bound for $Q(n,k)$ is improved for any $k\geq 5$ and the lower bound is improved for odd $k\geq 7$. Keywords: n-ary quasigroup, latin cube, loop, asymptotic estimate, component, latin trade.Comment: english 9pp, russian 9pp. v.2: corrected: initial data for recursion; added: Appendix with progra

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques