"The Number of Points in a Sliced Orthotope"

Thomas Zaslavsky
Binghamton University (SUNY)

Tuesday, March 30, 2010
1:00 pm
845 Patterson Office Tower

Abstract:

The number of integer lattice points in an orthotope (a higher-dimensional rectangle) is an easy calculation, but it becomes harder if we cut out all the points in a set of hyperplanes. Suppose the hyperplanes have the form xj = xi + cij , where cij is an integer. The problem is solvable by a graph-theoretic deletion-contraction argument if we treat the lattice points as proper colorations of "weighted integral gain graphs", which are graphs with complicated but pleasing decorations.