Discrete CATS Seminar
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U N I V E R S I T Y
O F
K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

SPRING 2010

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"The Number of Points in a Sliced Orthotope"

Thomas Zaslavsky

Binghamton University (SUNY)

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Tuesday, March 30, 2010

1:00 pm

845 Patterson Office Tower

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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.