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Abstract: Franek et al. recently described four constructions for large sets of -intersecting Steiner triple systems of order (STS ) [F. Franek, M.J. Grannell, T.S. Griggs, A. Rosa, On the large sets of -intersecting Steiner triple systems of order , Des. Codes Cryptogr. 26 (2002) 243–256]. In this study we focus on large sets of -intersecting STS . Some recursive constructions are presented that involve three-wise balanced designs. By applying these constructions we obtain some new infinite classes of such large sets, and the large sets of -intersecting KTS are used to produce some new large sets of Kirkman triple systems. [Copyright &y& Elsevier]

Abstract: An () over a -set is a collection of pairwise disjoint resolvable (almost resolvable) Mendelsohn triple systems of order . In this paper several direct construction methods for OLRMTSs and OLARMTSs are presented and then applied to produce some new orders; the smallest unknown for , the smallest unknown for , and some other small designs are displayed; a few new existence families are also obtained by known recursive constructions. [Copyright &y& Elsevier]

Abstract: We use discrete Morse theory to determine the Möbius function of generalized factor order. Ordinary factor order on the Kleene closure of a set is the partial order defined by letting if contains as a subsequence of consecutive letters. Generalized factor order takes into account a partial order on the alphabet , that is, whenever contains a subsequence such that for each , in . Using Babson and Hersh’s application of Robin Forman’s discrete Morse theory to poset order complexes, we are able to give a recursive formula for the Möbius function in the case where each element of covers a unique letter in . [Copyright &y& Elsevier]