Bijective counting of one-face maps on surfaces

  • Date: 11/17/2009
Guillaume Chapuy (Simon Fraser University)

University of British Columbia


A one-face map is a graph embedded in a compact surface, in such a way

that its complement is a topological disk. Dually, it can be viewed as a

polygon of even size, in which edges have been pasted pairwise to create a

surface. These objects have very nice enumerative properties, discovered

years ago by Lehman, Walsh, Harer and Zagier, but until very recently

their combinatorial interpretation remained mysterious.

I will present a bijection that enables us to understand the structure of

these objects better, and obtain all enumerative results very easily (in

particular the product formula counting one-face maps of given genus,

involving Catalan numbers). I will also present a recent extension made

jointly with Olivier Bernardi (MIT) to non-orientable surfaces.


4:00pm - 5:00pm, WMAX 216.