Operation of weaving partial Steiner triple systems

Abstract: We introduce an operation of a kind of product which associates with a partial Steiner triple system another partial Steiner triple system, the starting one being a quotient of the result. We discuss relations of our product to some other product-like constructions and prove some preservation/non-preservation theorems. In particular, we show series of anti-Pasch Steiner triple systems which are obtained that way.