Balanced labellings and Schubert polynomials

Sergey Fomin, Curtis Greene, Victor Reiner, Mark Shimozono

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24 Scopus citations

Abstract

We study Balanced labellings of diagrams representing the inversions in a permutation. These are known to be natural encodings of reduced decompositions of permutations w ∈ Σn, and we show that they also give combinatorial descriptions of both the Stanley symmetric functions Fw, and the Schubert polynomial G-fraktur signw associated with w. Furthermore, they lead to an explicit basis for the Schubert modules introduced by Kraskiewicz and Pragacz.

Original languageEnglish (US)
Pages (from-to)373-389
Number of pages17
JournalEuropean Journal of Combinatorics
Volume18
Issue number4
DOIs
StatePublished - May 1997

Bibliographical note

Funding Information:
The research of the authors was supported in part by NSF Grants DMS-9400914, DMS-9005666, DMS-9206371 and DMS-9407639, respectively.

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