Sara Billey ; Alexander Holroyd ; Benjamin Young - A bijective proof of Macdonald's reduced word formula

dmtcs:6412 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6412
A bijective proof of Macdonald's reduced word formulaArticle

Authors: Sara Billey 1; Alexander Holroyd 2; Benjamin Young 3

  • 1 Department of Mathematics [Seattle]
  • 2 Microsoft Research [Redmond]
  • 3 Department of Mathematics, University of Oregon [Eugene]

We describe a bijective proof of Macdonald's reduced word identity using pipe dreams and Little's bumping algorithm. The proof extends to a principal specialization of the identity due to Fomin and Stanley. Our bijective tools also allow us to address a problem posed by Fomin and Kirillov from 1997, using work of Wachs, Lenart and Serrano- Stump.

https://doi.org/10.46298/dmtcs.6412
Source: HAL:hal-02173737v1
Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Combinatorial and Algebraic Aspects of Varieties; Funder: National Science Foundation; Code: 1101017
  • Bio-based solvent identification and evaluation for use in polyurethane resin binders for the roofing industry; Funder: National Science Foundation; Code: 98052

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