Why Delannoy numbers?

Cyril Banderier (1) , Sylviane Schwer (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

This article is not a research paper, but a little note on the history of combinatorics: We present here a tentative short biography of Henri Delannoy, and a survey of his most notable works. This answers to the question raised in the title, as these works are related to lattice paths enumeration, to the so-called Delannoy numbers, and were the first general way to solve Ballot-like problems. These numbers appear in probabilistic game theory, alignments of DNA sequences, tiling problems, temporal representation models, analysis of algorithms and combinatorial structures.

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]; Histoire et perspectives sur les mathématiques [math.HO]; Algorithme et structure de données [cs.DS]; Statistiques [math.ST]; Génomique, Transcriptomique et Protéomique [q-bio.GN]; Informatique et théorie des jeux [cs.GT]

Cyril Banderier, Sylviane Schwer. Why Delannoy numbers?. Journal of Statistical Planning and Inference, 2005, 135 (1), pp.40-54. ⟨hal-00003233⟩