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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 269: Seminar in Combinatorics
Finn Southerland
UCSD
Region counting on another level
Abstract:
The number of regions of a hyperplane arrangement is a well-understood invariant, which we can complicate by counting regions of a given \emph{level}, a statistic quantifying a region's boundedness. Rediscovering a formula of Zaslavsky, we show that the level distribution is a \emph{combinatorial invariant}, and in the process define it for all semimatroids. The formula also allows us to reprove and generalize many known results on deformations of the braid arrangement.
January 27, 2026
2:00 PM
APM 7321
Research Areas
Combinatorics****************************
