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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Official URL: http://dx.doi.org/10.1007/s10801-007-0113-0
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 |
|---|---|
| ISSN: | 0925-9899 (print) |
| Uncontrolled Keywords: | jacobi-trudi determinant, jeu de taquin, ribbon, schubert calculus, schur positive, skew schur function, symmetric function |
| Related URLs: | http://dx.doi.org/10.1007/s108...007-0113-0 |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics |
| ePrint ID: | 66210 |
| Deposited On: | 12 Jan 2010 |
| Last Modified: | 01 Jun 2011 06:15 |
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