Date of Award
2018
Degree Name
Mathematics
College
College of Science
Type of Degree
M.A.
Document Type
Thesis
First Advisor
Dr. Elizabeth Niese, Committee Chairperson
Second Advisor
Dr. JiYoon Jung
Third Advisor
Dr. Carl Mummert
Abstract
The Knuth transformations on words, the jeu de taquin moves on tableaux, and the Robinson–Schensted–Knuth algorithm produce the same equivalence classes for words. By observing the connections between these three methods we find and prove there exists connections between the Assaf–Knuth transformations, our extension of the jeu de taquin, and p-RSK. We know there exists an algebraic way to expand Macdonald polynomials in terms of the Schur functions. The form of the expansion implies there should be a combinatorial way to find the expansion. Loehr found a Robinson–Schensted–Knuth like algorithm that works in some cases. By finding an extension of jeu de taquin, we will try to expand the number of cases covered.
Subject(s)
Times Play (Competition)
Combinatorial analysis.
Recommended Citation
McKinney, Joanna, "An Extension of the Jeu de Taquin" (2018). Theses, Dissertations and Capstones. 1189.
https://mds.marshall.edu/etd/1189
