Why Delannoy numbers?

Details Why Delannoy numbers? Why Delannoy numbers?

2004-11-06

arxiv.org/abs/math/0411128v1

Journal of Statistical Planning and Inference 135, 1 (11/2005) 40-54

Mathematics

Combinatorics

Presented to the conference "Lattice Paths Combinatorics and Discrete Distributions" (Athens, June 5-7, 2002) and to appear in

Scientific paper

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.

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