A Markov growth process for Macdonald's distribution on reduced words
Combinatorics
2014-09-30 v1
Abstract
We give an algorithmic-bijective proof of Macdonald's reduced word identity in the theory of Schubert polynomials, in the special case where the permutation is dominant. Our bijection uses a novel application of David Little's generalized bumping algorithm. We also describe a Markov growth process for an associated probability distribution on reduced words. Our growth process can be implemented efficiently on a computer and allows for fast sampling of reduced words. We also discuss various partial generalizations and links to Little's work on the RSK algorithm.
Keywords
Cite
@article{arxiv.1409.7714,
title = {A Markov growth process for Macdonald's distribution on reduced words},
author = {Benjamin Young},
journal= {arXiv preprint arXiv:1409.7714},
year = {2014}
}
Comments
16 pages, 5 figures