Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, July 04, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Benjamin Matschke

The width of 5-dimensional prismatoids

Santos' construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width greater than d. Santos, Stephen and Thomas (2012) have shown that this cannot occur in dimension d < 5. Motivated by this 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 non-Hirsch polytopes of dimension 20, rather than the original dimension 43.
- There are 5-prismatoids with n vertices and width Ω(√n) for arbitrarily large n. Hence, the width of 5-prismatoids is unbounded.

This is joint work with Francisco Santos and Christophe Weibel.

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