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Lattice path proof of the ribbon determinant formula for Schur functions

Published online by Cambridge University Press:  22 January 2016

Kazuo Ueno
Kazuo Ueno*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Showa-ku, Nagoya 466, Japan
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In this note we give a lattice path proof of the ribbon determinant formula for Schur functions ((1) below) which was originally formulated and proved in [2].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 124 , December 1991 , pp. 55 - 59
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[ 1 ] Gessel, I. M. and Viennot, G., Determinants, paths, and plane partitions, preprint, July 1989.Google Scholar
[ 2 ] Lascoux, A. and Pragacz, P., Ribbon Schur functions, Europ. J. Combinatorics, 9 (1988), 561–574.CrossRefGoogle Scholar
[ 3 ] Macdonald, I. G., Symmetric Functions and Hall Polynomials, Oxford Univ. Press, 1979.Google Scholar
[ 4 ] Stanton, D. and White, D., Constructive Combinatorics, Springer, New York, 1986.CrossRefGoogle Scholar
[ 5 ] Stembridge, J. R., Nonintersecting paths, Pfaffians, and plane partitions, Advances in Math., 83 (1990), 96–131.Google Scholar