Bijective counting of one-face maps on surfaces
- Date: 11/17/2009
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.
