Abstracts
for the Seminar

Spring 2024

**Speaker: **Fiona Young, Cornell University

**Title: **The essential bound of a $k$-polymatroid and applications to excluded minor problems

**Time:** 2:30 PM, Monday, January 29, 2024

**Place:** ZOOM

**Abstract:** The singleton and doubleton minors of a polymatroid encode a surprising amount of information about its structural complexity. Starting with a $k$-polymatroid $\rho$, we subtract from it as many maximally-separated matroids as possible. Let the result be an $m$-polymatroid; this gives rise to a notion of boundedness for $\rho$. When $k$ is sufficiently large, the bounds on the singleton and doubleton minors of $\rho$ completely determine the bound on $\rho$. Much of this is motivated and guided by the polytopal perspective of polymatroids. Our results provide an organized framework for thinking about polymatroid excluded minor problems.

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