Now showing items 1-6 of 6

    • A Complete Multipartite Basis for the Chromatic Symmetric Function 

      Crew, Logan; Spirkl, Sophie (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, ...
    • A deletion–contraction relation for the chromatic symmetric function 

      Crew, Logan; Spirkl, Sophie (Elsevier, 2020-10)
      We extend the definition of the chromatic symmetric function XG to include graphs G with a vertex-weight function w : V (G) --> N. We show how this provides the chromatic symmetric function with a natural deletion-contraction ...
    • Disproportionate Division 

      Crew, Logan; Narayanan, Bhargav; Spirkl, Sophie (Wiley, 2020-10-01)
      We study the disproportionate version of the classical cake-cutting 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, 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 ...
    • 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 Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function 

      Aliste-Prieto, José; Crew, Logan; Spirkl, Sophie; Zamora, José (The Electronic Journal of Combinatorics, 2021-04-09)
      This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version ofXB, show that this function admits a ...


      University of Waterloo Library
      200 University Avenue West
      Waterloo, Ontario, Canada N2L 3G1
      519 888 4883

      All items in UWSpace are protected by copyright, with all rights reserved.

      DSpace software

      Service outages