Colloquium Schedule for Fall 1998 |

Enumeration of m-ary cacti


Professor Pierre Leroux
University of Quebec




A cactus is a connected graph all of whose 2-connectedcomponents are polygons. An m-ary cactus is a plane embedded cactus consisting of m-gons whose vertices are cyclically m-colored 1,2,...,m counterclockwise within each polygon.

In this talk, I will show how to enumerate m-ary cacti having given vertex degree distributions. This problem is related to:

  • statistical mechanics,
  • factorizations of a circular permutation into m permutations having given cycle types,
  • the topological classification of complex polynomialshaving m critical values.