Two Variable Pfaffian Identities and Symmetric Functions
Thomas Sundquist
DOI: 10.1023/A:1022417201878
Abstract
We give sign-reversing involution proofs of a pair of two variable Pfaffian identities. Applications to symmetric function theory are given, including identities relating Pfaffians and Schur functions. As a corollary we are able to compute the plethysm p 2 ^\circ s k n p_2 \circ s_{k^n} .
Pages: 135–148
Keywords: Pfaffian; involution; Schur function; plethysm; root system
Full Text: PDF
References
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2. F. Brioschi, "Sur l'analogicentre une classe determinants d'ordre pair; et sur les determinants binaires," Crelle 52(1856), 133-141.
3. I.M. Gessel, "Tournaments and Vandermonde's determinant," J. of Graph Theory 3 (1979), 305-307.
4. I.G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon, 1979.
5. T. Muir, The Theory of Determinants in the Historical Order of Development, MacMillan and Co., London, 1911.
6. R.A. Proctor, Personal Communication, 1991.
7. J.R. Stembridge, "Non-intersecting paths, Pfaffians and plane partitions," Adv. in Math. 83 (1990), 96-131.
8. T.S. Sundquist, Pfaffians, Involutions, and Schur Functions, Ph.D. Thesis, University of Minnesota, 1992.