On (some) functional equations arising in enumerative combinatorics

Mireille Bousquet-Mélou

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-24, 2001


I shall try to convince the audience not to be shy with functional equation approaches in enumerative combinatorics. They not only solve (some) problems, but they often teach us a lot too. The proofs they provide for a specific problem might be less nice than more combinatorial proofs. But functional equation approaches sometimes give a unified description of apparently distinct problems, and the efforts we make to solve one specific functional equation often teach us what to do in a more generic case. The talk will be based on recent examples dealing with very classical combinatorial objects: lattice paths, maps, permutations.
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