Discrete CATS Seminar
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UNIVERSITY OF KENTUCKY **

DISCRETE CATS SEMINAR

DISCRETE MATH AND COMBINATORICS: ALGEBRAIC & TOPOLOGICAL SEMINAR

113 PATTERSON OFFICE TOWER

FALL 2007

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"Sweeping the cd-Index"

Carl Lee

University of Kentucky

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Monday, September 17, 2007

4:00 pm, 113 Patterson Office Tower

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Abstract:

The cd-index of a convex polytope concisely encodes information about
the flag-vector of the polytope --- the numbers of chains of faces of
all types. Stanley proved that the coefficients of the cd-index are
non-negative using the technique of S-shellings. By interpreting an
S-shelling of a polytope P in the context of its dual P^* we provide a
simple recursive way to compute the cd-index by sweeping a hyperplane
across P^*. In addition we offer a way to visualize a partition of
the flags of P^* into subsets counted by the coefficients of the
cd-index. Finally, we show how also the toric h-vector can be easily
computed from a hyperplane sweep, and hence directly from the
cd-index.