A simple proof of the Littlewood-Richardson rule and applications

We present a simple proof of the Littlewood-Richardson rule using a sign-reversing involution, and show that a similar involution provides a com-binatorial proof of the SXP algorithm of Chen, Garsia, and Remmel 2] which computes the Schur function expansion of the plethysm of a Schur function and a power sum symmetric function. The methods of this paper have also been applied to prove combinatorial formulas for the characters of coordinate rings of nilpotent conjugacy classes of matrices 14].