Browsing Combinatorics and Optimization by Subject "algebraic combinatorics"
Now showing items 1-6 of 6
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A Complete Multipartite Basis for the Chromatic Symmetric Function
(Society for Industrial and Applied Mathematics, 2021-11-15)In the vector space of symmetric functions, the elements of the basis of elementary symmetric functions are (up to a factor) the chromatic symmetric functions of disjoint unions of cliques. We consider their graph complements, ... -
Enumeration of Factorizations in the Symmetric Group: From Centrality to Non-centrality
(University of Waterloo, 2011-04-25)The character theory of the symmetric group is a powerful method of studying enu- merative questions about factorizations of permutations, which arise in areas including topology, geometry, and mathematical physics. This ... -
Modular relations of the Tutte symmetric function
(Elsevier, 2022-04)For a graph G, its Tutte symmetric function XBG generalizes both the Tutte polynomial TG and the chromatic symmetric function XG. We may also consider XB as a map from the t-extended Hopf algebra G[t] of labelled graphs ... -
On Enumerative Structures in Quantum Field Theory
(University of Waterloo, 2020-07-13)This thesis addresses a number of enumerative problems that arise in the context of quantum field theory and in the process of renormalization. In particular, the enumeration of rooted connected chord diagrams is further ... -
Partition Algebras and Kronecker Coefficients
(University of Waterloo, 2015-08-28)Classical Schur-Weyl duality relates the representation theory of the general linear group to the representation theory of the symmetric group via their commuting actions on tensor space. With the goal of studying Kronecker ... -
Sequences of Trees and Higher-Order Renormalization Group Equations
(University of Waterloo, 2019-08-27)In 1998, Connes and Kreimer introduced a combinatorial Hopf algebra HCK on the vector space of forests of rooted trees that precisely explains the phenomenon of renormalization in quantum field theory. This Hopf algebra ...