Geodesic
A bijective proof of Macdonald's reduced word formula
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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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. 
@article{DMTCS_2020_special_379_a94,
     author = {Billey, Sara and Holroyd, Alexander and Young, Benjamin},
     title = {A bijective proof of {Macdonald's} reduced word formula},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6412},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6412/}
}
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Billey, Sara; Holroyd, Alexander; Young, Benjamin. A bijective proof of Macdonald's reduced word formula. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6412. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6412/

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