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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 269 - Seminar in Combinatorics
Prof. Carly Klivans
Brown University
The Arboricity Polynomial
Abstract:
I will introduce a new matroid (graph) invariant: The Arboricity Polynomial. Arboricity is a numerical invariant first introduced by Nash-Williams, Tutte and Edmonds. It captures the minimum number of independent sets (forests) needed to decompose the ground set of a matroid (edges of a graph). The arboricity polynomial enumerates the number of such decompositions. We examine this counting function in terms of scheduling, Ehrhart theory, quasisymmetric functions, matroid polytopes and the permutohedral fan.
February 24, 2025
2:00 PM
APM 6402
Research Areas
Combinatorics****************************
