A Pieri Rule for Skew Shapes

Sami H. Assaf; Peter R. W. McNamara

A Pieri Rule for Skew Shapes

Sami H. Assaf
, Peter R. W. McNamara

Bucknell University

Berkeley Quantitative

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Journal	Default journal
Volume	118
State	Published - Jan 1 2011

Keywords

Pieri rule
skew Schur functions
Robinson-Schensted

Disciplines

Mathematics

Access to Document

http://www.facstaff.bucknell.edu/pm040/Papers/skewpieri.pdf

Cite this

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title = "A Pieri Rule for Skew Shapes",

abstract = " 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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AU - McNamara, Peter R. W.

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N2 - 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.

AB - 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.

KW - Pieri rule

KW - skew Schur functions

KW - Robinson-Schensted

UR - https://digitalcommons.bucknell.edu/fac_journ/52

UR - http://www.facstaff.bucknell.edu/pm040/Papers/skewpieri.pdf

M3 - Article

VL - 118

JO - Default journal

JF - Default journal

ER -

A Pieri Rule for Skew Shapes

Abstract

Keywords

Disciplines

Access to Document

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Cite this