Balanced labellings and Schubert polynomials

Sergey Fomin; Curtis Greene; Victor Reiner; Mark Shimozono

doi:10.1006/eujc.1996.0109

Balanced labellings and Schubert polynomials

Sergey Fomin, Curtis Greene, Victor Reiner, Mark Shimozono

Mathematics

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

33 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 ∈ Σ_n, and we show that they also give combinatorial descriptions of both the Stanley symmetric functions F_w, and the Schubert polynomial G-fraktur sign_w associated with w. Furthermore, they lead to an explicit basis for the Schubert modules introduced by Kraskiewicz and Pragacz.

Original language	English (US)
Pages (from-to)	373-389
Number of pages	17
Journal	European Journal of Combinatorics
Volume	18
Issue number	4
DOIs	https://doi.org/10.1006/eujc.1996.0109
State	Published - 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.

Access

10.1006/eujc.1996.0109

OpenUrl availability

Full text

Cite this

@article{847a63e7206e4e8d81830431c4aee93c,

title = "Balanced labellings and Schubert polynomials",

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.",

author = "Sergey Fomin and Curtis Greene and Victor Reiner and Mark Shimozono",

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.",

year = "1997",

month = may,

doi = "10.1006/eujc.1996.0109",

language = "English (US)",

volume = "18",

pages = "373--389",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

publisher = "Academic Press Inc.",

number = "4",

}

TY - JOUR

T1 - Balanced labellings and Schubert polynomials

AU - Fomin, Sergey

AU - Greene, Curtis

AU - Reiner, Victor

AU - Shimozono, Mark

N1 - Funding Information: The research of the authors was supported in part by NSF Grants DMS-9400914, DMS-9005666, DMS-9206371 and DMS-9407639, respectively.

PY - 1997/5

Y1 - 1997/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21744457356&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21744457356&partnerID=8YFLogxK

U2 - 10.1006/eujc.1996.0109

DO - 10.1006/eujc.1996.0109

M3 - Article

AN - SCOPUS:21744457356

SN - 0195-6698

VL - 18

SP - 373

EP - 389

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 4

ER -

Balanced labellings and Schubert polynomials

Abstract

Bibliographical note

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this