A simple proof of the Littlewood-Richardson rule and applications Original Research Article

We present a simple proof of the Littlewood-Richardson rule using a sign-reversing involution, and show that a similar involution provides a combinatorial proof of the SXP algorithm of Chen et al. (1984) 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 (Shimozono, 1998).