Browsing Mathematics (Faculty of) by Author "Crew, Logan"
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A Complete Multipartite Basis for the Chromatic Symmetric Function
Crew, Logan; Spirkl, Sophie (Society for Industrial and Applied Mathematics, 20211115)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, ... 
A deletion–contraction relation for the chromatic symmetric function
Crew, Logan; Spirkl, Sophie (Elsevier, 202010)We extend the definition of the chromatic symmetric function XG to include graphs G with a vertexweight function w : V (G) > N. We show how this provides the chromatic symmetric function with a natural deletioncontraction ... 
Disproportionate Division
Crew, Logan; Narayanan, Bhargav; Spirkl, Sophie (Wiley, 20201001)We study the disproportionate version of the classical cakecutting problem: how efficiently can we divide a cake, here [0,1], among n ≥ 2 agents with different demands α1, α2,..., αn summing to 1? When all the agents have ... 
Modular relations of the Tutte symmetric function
Crew, Logan; Spirkl, Sophie (Elsevier, 202204)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 textended Hopf algebra G[t] of labelled graphs ... 
Plethysms of Chromatic and Tutte Symmetric Functions
Spirkl, Sophie; Crew, Logan (The Electronic Journal of Combinatorics, 2022)Plethysm is a fundamental operation in symmetric function theory, derived directly from its connection with representation theory. However, it does not admit a simple combinatorial interpretation, and finding coefficients ... 
A VertexWeighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function
AlistePrieto, José; Crew, Logan; Spirkl, Sophie; Zamora, José (The Electronic Journal of Combinatorics, 20210409)This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertexweighted version ofXB, show that this function admits a ...