Sami Assaf, Peter R. W. McNamara, Thomas Lam
Published 2009-08-03, updated 2010-04-26Version 2
The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in terms of skew Schur functions. Like the classical rule, our rule involves simple additions of boxes to the original skew shape. Our proof is purely combinatorial and extends the combinatorial proof of the classical case.
Comments: 19 pages, 2 figures. Main body is by Assaf and McNamara, appendix is by Lam. Updated to reflect proof of Conjecture 6.1 by Lam, Lauve and Sottile in arXiv:0908.3714. Final version, to appear in Journal of Combinatorial Theory (Series A)
Journal: Journal of Combinatorial Theory (Series A), 118 (1) (2011), 277-290
Equality of Schur and skew Schur functions
Coincidences among skew Schur functions
Commutation and normal ordering for operators on symmetric functions
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