Reduced words and a formula of MacdonaldAlgebra & Discrete Mathematics
|Sara Billey, U Washington
|Mon, Jan 25 2016, 1:10PM
Macdonald gave a remarkable formula connecting a weighted sum of reduced words for a permutation with the number of terms in a Schubert polynomial. We will review some of the fascinating results on the set of reduced words in order to put our main results in context. The main result is a new 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. This approach has been sought for over 20 years. Our bijective tools also allow us to address a problem posed by Fomin and Kirillov from 1997 using work of Wachs, Lenart, Serrano and Stump. This project extends earlier work by the third author on a Markov process for reduced words of the longest permutation.
This is joint work with Ben Young and Alexander Holroyd.
Prof Billey is around all Monday and much of Tues. Email Monica or her to set up some time to talk research!