A bijective proof of Macdonald's reduced word formula
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]
Abstract
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.
