A Pieri rule for skew shapes

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Assaf, Sami
McNamara, Peter R. W.
Lam, Thomas
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Abstract
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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.
Comment: 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)
Keywords
Mathematics - Combinatorics, 05E05 (Primary) 05E10, 20C30 (Secondary)
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