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

Symmetric quasigroups of odd order

AbstractQuasigroups of yet another type turn out to be related to Steiner Triple Systems, though the connection is rather loose and not as precise as in the various coordinatizing bijections described in [3]. However, families of pairs formed by abelian groups of odd order and quasigroups defined on the same set of elements have repeatedly been used in the literature to construct Large Sets [8] of Steiner Triple Systems. In Section 1, these quasigroups and their association with abelian groups are described, while Section 2 is devoted to applications to STSs

Two conjectures of Demetrovics, Füredi, and Katona, concerning partitions

AbstractIt is possible to find n partitions of an n-element set whose pairwise intersections are just all atoms of the partition lattice? Demetrovics, Füredi and Katona [4] verified this for all n ≡ 1 or 4 (mod 12) by constructing a series of special Mendelsohn Triple Systems. They conjectured that such triple systems exist for all n ≡ 1 (mod 3) and that the problem on the partitions has a solution for all n ⩾ 7. We prove that both conjectures are ture, except for finitely many n

Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results

We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of $t$ mutually orthogonal Latin squares of order $n$ to construct a set of $2t$ mutually orthogonal Latin squares of order $n^t$

Mathematical applications of inductive logic programming

Accepted versio