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.