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                * Princeton Discrete Math Seminar *
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Date: Thursday 29th March, 2.15 in Fine Hall 224
 
Speaker: Benjamin Matschke, IAS

Title: On the diameter of polytopes

Santos' construction of counter-examples to the Hirsch conjecture is
based on the existence of prismatoids of dimension d of width greater
than d. The case d=5 being the smallest one in which this can possibly
occur, we here study the width of 5-dimensional prismatoids, obtaining
the following results:
 
- There are 5-prismatoids of width six with only 25 vertices, versus
the 48 vertices in Santos' original construction. This leads to
lowering the dimension of the non-Hirsch polytopes from 43 to only 20.

 - There are 5-prismatoids with n vertices and width \Omega(n^(1/2))
for arbitrarily large n.

This is joint work with Francisco Santos and Christophe Weibel.

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Next week: Jeff Kahn

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