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Plane trivalent trees and their patterns

Charles Delorme — 2010

Open Mathematics

The aim of this paper is to characterize the patterns of successive distances of leaves in plane trivalent trees, and give a very short characterization of their parity pattern. Besides, we count how many trees satisfy some given sequences of patterns.

Sur la formule d’inversion de Lagrange

Charles Delorme — 2007

Annales de la faculté des sciences de Toulouse Mathématiques

On se propose de démontrer que la formule d’inversion de Lagrange est encore valide sur un anneau commutatif, même pour une série ayant quelques termes à coefficients nilpotents avant le terme de degré 1 (dont le coefficient est inversible). On n’use que de techniques algébriques.

On a problem of walks

Charles DelormeMarie-Claude Heydemann — 1999

Annales de l'institut Fourier

In 1995, F. Jaeger and M.-C. Heydemann began to work on a conjecture on binary operations which are related to homomorphisms of De Bruijn digraphs. For this, they have considered the class of digraphs G such that for any integer k , G has exactly n walks of length k , where n is the order of G . Recently, C. Delorme has obtained some results on the original conjecture. The aim of this paper is to recall the conjecture and to report where all the authors arrived.

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