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.