Coxeter-Knuth graphs and a signed little map for type B reduced words

Sara Billey, Zachary Hamaker, Austin Roberts, Benjamin Young

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 Kraśkiewicz 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.

Original languageEnglish (US)
Article numberP4.6
JournalElectronic Journal of Combinatorics
Volume21
Issue number4
DOIs
StatePublished - Oct 2 2014

Bibliographical note

Publisher Copyright:
© 2014, Australian National University. All rights reserved.

Keywords

  • Coxeter groups
  • Dual equivalence graphs
  • Kraśkiewicz insertion
  • Little map
  • Quasisymmetric functions
  • Reduced decompositions
  • Schur P-functions
  • Shifted tableaux
  • Stanley symmetric functions

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