Campus Event Calendar
Event Entry
What and Who
A connection of the chromatic polynomial to geometry
Roberto Henschel
AG1 Mittagsseminar (own work)
AG 1
AG Audience
English
Note: We use this to send email in the morning.
Date, Time and Location
Tuesday, 30 April 2013
13:00
60 Minutes
E1 4
024
Saarbrücken
Abstract
Beck und Zaslavsky show in [1], that the number of proper t-colorings
of a graph G=(V,E) equals the number of lattice points, which lay
inside the (t-1)-th dilation of a certain polytops P(G), but not on
any hyperplane of a specific hyperplane arrangement H(G). The exact
result, using Ehrhart's theory is being explained during the talk. It
will be analysed, which cells of the polytope, induced by the
seperation of the hyperplane arrangement, induce the same Ehrhart
polynomial. As an application, the chromatic polynomial of a path is
derived using the Ansatz of Beck und Zaslavsky.
[1]=Beck, M. ; Zaslavsky, T.: Inside-out polytopes. In: Advances in
Mathematics 205 (2006), Nr. 1, S. 134–162. – ISSN 0001–8708
of a graph G=(V,E) equals the number of lattice points, which lay
inside the (t-1)-th dilation of a certain polytops P(G), but not on
any hyperplane of a specific hyperplane arrangement H(G). The exact
result, using Ehrhart's theory is being explained during the talk. It
will be analysed, which cells of the polytope, induced by the
seperation of the hyperplane arrangement, induce the same Ehrhart
polynomial. As an application, the chromatic polynomial of a path is
derived using the Ansatz of Beck und Zaslavsky.
[1]=Beck, M. ; Zaslavsky, T.: Inside-out polytopes. In: Advances in
Mathematics 205 (2006), Nr. 1, S. 134–162. – ISSN 0001–8708
Contact
Andreas Karrenbauer
--email hidden
passcode not visible
logged in users only
Andreas Karrenbauer, 04/28/2013 23:51 -- Created document.