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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Towards a combinatorial classification of skew Schur functions


Authors: Peter R. W. McNamara and Stephanie van Willigenburg
Journal: Trans. Amer. Math. Soc. 361 (2009), 4437-4470
MSC (2000): Primary 05E05; Secondary 05E10, 20C30
Published electronically: March 9, 2009
MathSciNet review: 2500893
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Abstract: We present a single operation for constructing skew diagrams whose corresponding skew Schur functions are equal. This combinatorial operation naturally generalises and unifies all results of this type to date. Moreover, our operation suggests a closely related condition that we conjecture is necessary and sufficient for skew diagrams to yield equal skew Schur functions.


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Additional Information

Peter R. W. McNamara
Affiliation: Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
Address at time of publication: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
Email: peter.mcnamara@bucknell.edu

Stephanie van Willigenburg
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada
Email: steph@math.ubc.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04683-2
PII: S 0002-9947(09)04683-2
Keywords: Jacobi-Trudi determinant, Hamel-Goulden determinant, ribbon, symmetric function, skew Schur function, Weyl module
Received by editor(s): June 30, 2007
Received by editor(s) in revised form: November 15, 2007
Published electronically: March 9, 2009
Additional Notes: The second author was supported in part by the National Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.