Relating Edelman–Greene insertion to the Little map

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• 作者：Zachary Hamaker ; Benjamin Young
• 关键词：Reduced words ; Little map ; Edelman–Greene ; Stanley symmetric functions ; Dual equivalence ; Sorting network ; Coxeter–Knuth move ; Robinson–Schensted algorithm
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2014
• 出版时间：November 2014
• 年：2014
• 卷：40
• 期：3
• 页码：693-710
• 全文大小：463 KB
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• 作者单位：Zachary Hamaker (1)
  Benjamin Young (2)
  
  1. Department of Mathematics, Dartmouth College, 27 N. Main Street, 6188 Kemeny Hall, Hanover, NH, 03755-3551, USA
  2. Department of Mathematics, 1222 University of Oregon, Eugene, OR, 97403-1205, USA
  
• ISSN：1572-9192

文摘

The Little map and the Edelman–Greene insertion algorithm, a generalization of the Robinson–Schensted correspondence, are both used for enumerating the reduced decompositions of an element of the symmetric group. We show the Little map factors through Edelman–Greene insertion and establish new results about each map as a consequence. In particular, we resolve some conjectures of Lam and Little.