A Pieri rule for skew shapes

Details A Pieri rule for skew shapes A Pieri rule for skew shapes

2009-08-03

arxiv.org/abs/0908.0345v2

Journal of Combinatorial Theory (Series A), 118 (1) (2011), 277-290

Mathematics

Combinatorics

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

Scientific paper

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.

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