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1993 RC-graphs and Schubert polynomials
Nantel Bergeron, Sara Billey
Experiment. Math. 2(4): 257-269 (1993).

Abstract

Using a formula of Billey, Jockusch and Stanley, Fomin and Kirillov have introduced a new set of diagrams that encode the Schubert polynomials. We call these objects rc-graphs. We define and prove two variants of an algorithm for constructing the set of all rc-graphs for a given permutation. This construction makes many of the identities known for Schubert polynomials more apparent, and yields new ones. In particular, we give a new proof of Monk's rule using an insertion algorithm on rc-graphs. We conjecture two analogs of Pieri's rule for multiplying Schubert polynomials. We also extend the algorithm to generate the double Schubert polynomials.

Citation

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Nantel Bergeron. Sara Billey. "RC-graphs and Schubert polynomials." Experiment. Math. 2 (4) 257 - 269, 1993.

Information

Published: 1993
First available in Project Euclid: 24 March 2003

zbMATH: 0803.05054
MathSciNet: MR1281474

Subjects:
Primary: 05E99
Secondary: 05E05 , 14M15 , 20C30

Rights: Copyright © 1993 A K Peters, Ltd.

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Vol.2 • No. 4 • 1993
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