. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi CHAPTER 1. A GENERAL OVERVIEW AND INTRODUCTION . . . . 1 CHAPTER 2. PRELIMINARIES: COMMUTATIVE ASSOCIATION SCHEMES AND THEIR TERWILLIGER ALGEBRAS . . . . . . . . . . . . . . . . . 4 2.1 The Bose-Mesner Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The Dual Bose-Mesner Algebra . . . . . . ....

This paper is based on an hour address given at the Sixth Conference on Formal Power Series and Algebraic Combinatorics, held at DIMACS in 1994. It is written primarily for an audience of combinato-rialists. Our hope is to publicise some intriguing enumerative conjectures which arise in the study of the homology representations of the poset of (set) partitions with an even number of blocks. The...

Let m be a positive integer and let ? finite set. The m-closure of G ? Sym(?) is the largest permutation group G(m) on having same orbits as in its induced action Cartesian product ?m. An exact formula for wreath given. As corollary, sufficient condition obtained this to included m-closures factors.