The Saga of Reduced Factorizations of Elements of the Symmetric Group

These notes cover the contents of a series of lectures in a Topics in Algebraic Combinatorics course given at UCSD in Winter 2001. The initial efiort was prompted by a desire to understand the connections between the theory of reduced decompositions started by the pioneering paper [] of R. Stanley and the theory of balanced tabloids studied by C. Green et al. [] [] However soon it appeared quite clear that a deeper understanding of the sub