Geodesic
Coxeter-Knuth graphs and a signed little map for type B reduced words
Sara Billey1 ; Zachary Hamaker2 ; Austin Roberts3 ; Benjamin Young4
1University of Washington
2Institute for Mathematics and its Applications
3Highline College
4University of Oregon
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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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.
DOI : 10.37236/4384
Classification : 05A05, 05A19, 05E05
Mots-clés : Stanley symmetric functions, Coxeter groups, reduced decompositions, shifted tableaux, dual equivalence graphs, Little map, Kraśkiewicz insertion, quasisymmetric functions, Schur \(P\)-functions

Sara Billey  1   ; Zachary Hamaker  2   ; Austin Roberts  3   ; Benjamin Young  4

1 University of Washington
2 Institute for Mathematics and its Applications
3 Highline College
4 University of Oregon 
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     author = {Sara Billey and Zachary Hamaker and Austin Roberts and Benjamin Young},
     title = {Coxeter-Knuth graphs and a signed little map for type {B} reduced words},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {4},
     doi = {10.37236/4384},
     zbl = {1298.05006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4384/}
}
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Sara Billey; Zachary Hamaker; Austin Roberts; Benjamin Young. Coxeter-Knuth graphs and a signed little map for type B reduced words. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4384

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