A bijective proof of Macdonald’s reduced word formula

Billey, Sara C.; Holroyd, Alexander E.; Young, Benjamin J.

doi:10.5802/alco.23

Billey, Sara C.¹ ; Holroyd, Alexander E.² ; Young, Benjamin J.³

¹ Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA
² Microsoft Research, 1 Microsoft Way, Redmond, WA 98052, USA
³ Department of Mathematics, 1222 University of Oregon, Eugene, OR 97403, USA

Algebraic Combinatorics, Tome 2 (2019) no. 2, pp. 217-248.

Résumé

We give a bijective proof of Macdonald’s reduced word identity using pipe dreams and Little’s bumping algorithm. This proof extends to a principal specialization due to Fomin and Stanley. Such a proof has been sought for over 20 years. Our bijective tools also allow us to solve a problem posed by Fomin and Kirillov from 1997 using work of Wachs, Lenart, Serrano and Stump. These results extend earlier work by the third author on a Markov process for reduced words of the longest permutation.

Reçu le : 2017-08-30
Accepté le : 2018-05-29
Publié le : 2019-03-05

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/alco.23

Affiliations des auteurs :

Billey, Sara C. ¹ ; Holroyd, Alexander E. ² ; Young, Benjamin J. ³

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Billey, Sara C.; Holroyd, Alexander E.; Young, Benjamin J. A bijective proof of Macdonald’s reduced word formula. Algebraic Combinatorics, Tome 2 (2019) no. 2, pp. 217-248. doi : 10.5802/alco.23. http://www.numdam.org/articles/10.5802/alco.23/

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