Dual Equivalence Graphs and their Applications
Thesis (Ph.D.)--University of Washington, 2014 In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's fundamental quasisymmetric...
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ftunivwashington:oai:digital.lib.washington.edu:1773/26525 2023-05-15T18:11:27+02:00 Dual Equivalence Graphs and their Applications Roberts, Austin Billey, Sara 2014 application/pdf http://hdl.handle.net/1773/26525 en_US eng Roberts_washington_0250E_12972.pdf http://hdl.handle.net/1773/26525 Copyright is held by the individual authors. combinatorics dual equivalence graphs Hall-Littlewood Macdonald polynomials schur functions symmetric functions Mathematics Thesis 2014 ftunivwashington 2023-03-12T18:51:45Z Thesis (Ph.D.)--University of Washington, 2014 In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's fundamental quasisymmetric functions in such a way that the sum of the weights of a connected component is a single Schur function. The graphs are termed dual equivalence graphs, and this dissertation is the compilation of works that focus on the further development of the theory of said graphs. This work further includes applications to Macdonald polynomials, Hall-Littlewood polynomials, and Lascoux-Leclerc-Thibon polynomials. In joint work with Sara Billey, Zach Hamaker, and Benjamin Young, we also give a generalization of dual equivalence graphs to the Coxeter-Knuth graph of Lie type B and illustrate the relationship of these graphs to a newly defined type B Little bump. For the sake of completeness, we also include an appendix providing a proof of the original axiomatization of dual equivalence graphs as described by Sami Assaf. Thesis sami University of Washington, Seattle: ResearchWorks |
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Open Polar |
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University of Washington, Seattle: ResearchWorks |
op_collection_id |
ftunivwashington |
language |
English |
topic |
combinatorics dual equivalence graphs Hall-Littlewood Macdonald polynomials schur functions symmetric functions Mathematics |
spellingShingle |
combinatorics dual equivalence graphs Hall-Littlewood Macdonald polynomials schur functions symmetric functions Mathematics Roberts, Austin Dual Equivalence Graphs and their Applications |
topic_facet |
combinatorics dual equivalence graphs Hall-Littlewood Macdonald polynomials schur functions symmetric functions Mathematics |
description |
Thesis (Ph.D.)--University of Washington, 2014 In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's fundamental quasisymmetric functions in such a way that the sum of the weights of a connected component is a single Schur function. The graphs are termed dual equivalence graphs, and this dissertation is the compilation of works that focus on the further development of the theory of said graphs. This work further includes applications to Macdonald polynomials, Hall-Littlewood polynomials, and Lascoux-Leclerc-Thibon polynomials. In joint work with Sara Billey, Zach Hamaker, and Benjamin Young, we also give a generalization of dual equivalence graphs to the Coxeter-Knuth graph of Lie type B and illustrate the relationship of these graphs to a newly defined type B Little bump. For the sake of completeness, we also include an appendix providing a proof of the original axiomatization of dual equivalence graphs as described by Sami Assaf. |
author2 |
Billey, Sara |
format |
Thesis |
author |
Roberts, Austin |
author_facet |
Roberts, Austin |
author_sort |
Roberts, Austin |
title |
Dual Equivalence Graphs and their Applications |
title_short |
Dual Equivalence Graphs and their Applications |
title_full |
Dual Equivalence Graphs and their Applications |
title_fullStr |
Dual Equivalence Graphs and their Applications |
title_full_unstemmed |
Dual Equivalence Graphs and their Applications |
title_sort |
dual equivalence graphs and their applications |
publishDate |
2014 |
url |
http://hdl.handle.net/1773/26525 |
genre |
sami |
genre_facet |
sami |
op_relation |
Roberts_washington_0250E_12972.pdf http://hdl.handle.net/1773/26525 |
op_rights |
Copyright is held by the individual authors. |
_version_ |
1766184108820529152 |