Coxeter-Knuth graphs and a signed Little map for type B reduced words
Abstract
We define an analog of David Little's algorithm for reduced words in type B, and investigate its main properties. In particular, we show that our algorithm preserves the recording tableau of Kra\'{s}kiewicz insertion, and that it provides a bijective realization of the Type B transition equations in Schubert calculus. Many other aspects of type A theory carry over to this new setting. Our primary tool is a shifted version of the dual equivalence graphs defined by Assaf and further developed by Roberts. We provide an axiomatic characterization of shifted dual equivalence graphs, and use them to prove a structure theorem for the graph of Type B Coxeter-Knuth relations.
Keywords
Cite
@article{arxiv.1405.4891,
title = {Coxeter-Knuth graphs and a signed Little map for type B reduced words},
author = {Sara Billey and Zachary Hamaker and Austin Roberts and Benjamin Young},
journal= {arXiv preprint arXiv:1405.4891},
year = {2014}
}
Comments
41 pages, 10 figures, many improvements from version 1, substantively the same as the version in Electronic Journal of Combinatorics, Vol 21, Issue 4