A Bijective Proof of Macdonald’s Reduced Word Formula
- Sara C. Billey ,
- Alexander E. Holroyd ,
- Benjamin J. Young
FPSAC 2016 Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics |
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.