Algebra and Combinatorics Seminar

Date: February 15, 2019

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Galen Dorpalen-Barry, University of Minnesota

Title: Whitney Numbers for Cones

Abstract: An arrangement of hyperplanes dissects space into connected components called chambers. A nonempty intersection of halfspaces from the arrangement will be called a cone.  The number of chambers of the arrangement lying within the cone is counted by a theorem of Zaslavsky, as a sum of certain nonnegative integers that we will call the cone's "Whitney numbers of the 1st kind".  For cones inside the reflection arrangement of type A (the braid arrangement), cones correspond to posets, chambers in the cone correspond to linear extensions of the poset, and these Whitney numbers refine the number of linear extensions.  We present some basic facts about these Whitney numbers, and interpret them for two families of posets.