Model theory of Steiner triple systems

A Steiner triple system (STS) is a set S together with a collection B of subsets of S of size 3 such that any two elements of S belong to exactly one element of B. It is well known that the class of finite STS has a Fraïssé limit MF. Here, we show that the theory T*Sq of MF is the model completion of the theory of STSs. We also prove that T*Sq is not small and it has quantifier elimination, TP2, NSOP1, elimination of hyperimaginaries and weak elimination of imaginaries

Constructions of new matroids and designs over GF(q)

A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same size. In this paper we introduce the q-analogue of a PMD and its properties. In order to do that, we first establish a new cryptomorphic definition for q-matroids. We show that q-Steiner systems are examples of q-PMD's and we use this q-matroid structure to construct subspace designs from q-Steiner systems. We apply this construction to S(2, 3, 13; q) q-Steiner systems and hence establish the existence of subspace designs with previously unknown parameters

An extensive English language bibliography on graph theory and its applications, supplement 1

Graph theory and its applications - bibliography, supplement