Abstract
A new combinatorial rule for expanding the product of Schur functions as a sum of Schur functions is formulated. The rule has several advantages over the Littlewood-Richardson rule (D. E. Littlewood and A. R. Richardson, Philos. Trans. Roy. Soc. London Ser. A 233 (1934), 49–141). First this rule allows for direct computation of the expansion of the product of any number of Schur functions, not just the product of two Schur functions. Also, the rule is easily stated and is well suited to computer implementation. It is shown that the rule implies the Littlewood-Richardson rule and gives a combinatorial proof that the coefficient of S λ in the product S μ S ν equals the coefficient of S ν in the expansion of the skew Schur function S λ μ . The rule is derived from some results proved independently by A. P. Hillman and R. M. Grassl ( J. Combin. Comput. Sci. Systems 5 (1980), 305–316) and by D. White ( J. Combin. Theory Ser. A 30 (1981), 237–247) on the Robinson-Schensted-Knuth correspondence.
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