Title: 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 level, a statistic that quantifies each region’s "boundedness." Rediscovering a formula of Zaslavsky, we show that the level distribution is a combinatorial invariant and in the process define it for all semi-matroids. The formula allows us to reprove and generalize results on deformations of the braid arrangements and certain specializations beg for alternate interpretations. Joint work with Lani Southern and Su Zhou.