Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes


King, Ronald C., Welsh, Trevor A. and van Willigenberg, Stephanie J. (2008) Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes. Journal of Algebraic Combinatorics, 28, 139-167. (doi:10.1007/s10801-007-0113-0).

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Description/Abstract

Some new relations on skew Schur function differences are
established both combinatorially using Sch\"utzenberger's jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences
of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1007/s10801-007-0113-0
ISSNs: 0925-9899 (print)
Related URLs:
Keywords: jacobi-trudi determinant, jeu de taquin, ribbon, schubert calculus, schur positive, skew schur function, symmetric function
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
ePrint ID: 66210
Date :
Date Event
August 2008Published
Date Deposited: 12 Jan 2010
Last Modified: 31 Mar 2016 12:52
URI: http://eprints.soton.ac.uk/id/eprint/66210

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