A Pieri rule for skew shapes

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 r...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series A 2011, Vol.118 (1), p.277-290
Main Authors: Assaf, Sami H., McNamara, Peter R.W.
Format: Article
Language:English
Subjects:
Pieri rule
Robinson–Schensted
Skew Schur functions
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Summary: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.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2010.03.010