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Quadratic forms of skew Schur functions. (English) Zbl 0651.05011
The skew Schur function is a generating function for skew column-strict plane partitions. The author uses non-intersecting path representations of such partitions to prove a quadratic identity for skew Schur functions. Such expansions had been proved by A. Lascoux (unpublished) using the Jacobi-Trudi identity and work with determinants. The author derives a family of quadratic expansions for the product of an arbitrary pair of skew Schur functions, a special case of which is the main result of Lascoux.
Reviewer: G.L.Alexanderson

MSC:
05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
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[1] De Concini, C. and Lascoux, A., Lettre ouverte sur les fonctions de Schur et equations de Plücker, preprint.
[2] Gessel, I. and Viennot, G., Determinants and plane partitions, preprint. · Zbl 0579.05004
[3] Goulden, I.P.; Jackson, D.M., Combinatorial enumeration, (1983), J. Wiley New York · Zbl 0519.05001
[4] Lascoux, A. Private communication.
[5] Macdonald, I.G., Symmetric functions and Hall polynomials, (1979), Clarendon Press Oxford · Zbl 0487.20007
[6] Stanley, R.P., Theory and application of plane partitions I., II, Studies applied math, 50, 167-188, (1971), 259-279 · Zbl 0225.05011
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