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Introduction to species and combinatorial equations

Monday 7th April 2008 - 10:00 to 11:11
INI Seminar Room 1

1) Elementary introduction to species through examples : Collecting structures into species leading to the general definition of a combinatorial species. Exponential generating series of a species for labelled enumeration. Elementary combinatorial operations and equations between species.

2) More advanced theory : Cycle index and tilda series of a species for unlabelled enumeration. Equipotence versus combinatorial equality. Taking connected components. Combinatorial equations for weighted connected and 2-connected graphs. Explicit examples.

*Note : This lecture is preparatory to the reading of papers of Pierre Leroux and collaborators. These papers are available below. Other material, including a link to the book "Combinatorial Species and Tree-like Structures", can be found on Pierre Leroux's web page

Introduction to the Theory of Species of Structures, by François Bergeron, Gilbert Labelle, and Pierre Leroux.

Papers and slides on Mayer graph weights:

Papers and slides on two-connected graphs:

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons