\(NS1D0\) Sequences and Anti-Pasch Steiner Triple Systems

Feliu Sagols1, Charles J. Colbourn2
1Electrical Engineering CINVESTAV, México
2Computer Science University of Vermont Burlington, VT 05405, U.S.A.

Abstract

We present an algorithmic construction of anti-Pasch Steiner triple systems for orders congruent to \(9\) mod \(12\). This is a Bose-type method derived from a particular type of \(3\)-triangulations generated from non-sum-one-difference-zero sequences (\(NS1D0\) sequences). We introduce \(NS1D0\) sequences and describe their basic properties; in particular, we develop an equivalence between the problem of finding \(NS1D0\) sequences and a variant of the \(n\)-queens problem. This equivalence, and an algebraic characterization of the \(NS1D0\) sequences that produce anti-Pasch Steiner triple systems, form the basis of our algorithm.