zbMATH — the first resource for mathematics

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 Such expansions had been proved by A. Lascoux (unpublished) using the Jacobi-Trudi identity and work with determinants.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

05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.