Combinatorics Seminar

Spring 2006

The seminar is on Thursdays at 11:00 AM in Bradley 105.

The seminar will be followed by the Thursday Lunch Expedition.

May 19, 2006
Christophe Hohlweg (The Fields Institute, University of TOronto)

Title:
  Realizations of the associahedron and cyclohedron

SPECIAL ROOM: Bradley 104 and TIME: 4:00 PM

Abstract: We describe different realizations with integer coordinates for
the associahedron (i.e., the Stasheff polytope) and for the cyclohedron
(i.e., the Bott-Taubes polytope), and compare them to the permutahedra of
type $A$ and $B$, respectively.

The coordinates are integral and obtained by an algorithm which uses an
oriented Coxeter graph of type $A$ or $B$ respectively as the only input and
which specializes to a procedure presented by J.-L. Loday for a certain
orientation of the Coxeter graph of $A_n$.

The described realizations have cambrian fans of type $A$ and $B$ as normal
fans. This settles a conjecture of N. Reading for cambrian fans of these
types.

This is a joint work with Carsten Lange.

May 17, 2006
Peter Winkler (Dartmouth)

Title:
 Non-Transitive Dice II

Abstract: Continuation of Non-Transitive Dice from last Thurday, with special
presentation by Annalies Vuong that the upper bound for the size of a dominating
set for a 2-majority tournament is 3.

May 11, 2006
Peter Winkler (Dartmouth)

Title:
 Non-Transitive Dice

Abstract: Starting with an old scam, we will see how some modern combinatorial methods
(including VC-dimension) can be used to attack problems in graph theory and geometry.
The intention is to go slowly and take 2 or 3 weeks as necessary.

April 13, 2006
Carsten Lange (University of Washington)

Title:
 Lower bounds for chromatic number

Abstract: A famous problem is the 4-colour problem: How many colours do we need
to colour the countries of a map such that two neighbouring countries are
always assigned different colours?

This task to find the chromatic number of a (hyper-)graph is very hard.
Lovasz introduced a ``topological method'' to obtain lower bounds. I will
introduce this subject and discuss the method.




If you are intenterested in speaking please email Rosa.C.Orellana "at" Dartmouth "dot" edu

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