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Lattice Paths and a Sergeev-Pragacz Formula for Skew Supersymmetric Functions

Published online by Cambridge University Press:  20 November 2018

A. M. Hamel  and
I. P. Goulden
A. M. Hamel*
Affiliation:
Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N2L 3G1
I. P. Goulden
Affiliation:
Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N2L 3G1
*
Current address for first author: Department of Mathematics and Statistics University of Canterbury Christchurch, New Zealand
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Abstract

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We obtain a new version of the Sergeev–Pragacz formula for supersymmetric functions of standard shape–one applicable to arbitrary skew shape. The result involves an antisymmetrized sum of determinants that are themselves flagged supersymmetric functions. The proof is combinatorial, and follows by means of lattice path transformations.

Keywords

05E0505A1515A15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 2 , 01 April 1995 , pp. 364 - 382
Copyright
Copyright © Canadian Mathematical Society 1995

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