Why Delannoy numbers?
<|reference_start|>Why Delannoy numbers?: 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.<|reference_end|>
@article{banderier2004why,
    title={Why Delannoy numbers?},
    author={Cyril Banderier (LIPN), Sylviane Schwer (LIPN)},
    journal={Journal of Statistical Planning and Inference 135, 1 (11/2005)
  40-54},
    year={2004},
    doi={10.1016/j.jspi.2005.02.004},
    archivePrefix={arXiv},
    eprint={math/0411128},
    primaryClass={math.CO cs.DS cs.GT math.HO math.PR math.ST q-bio.GN stat.TH}
}