Gapped Pattern Statistics

Philippe Duchon (1) , Cyril Nicaud (2) , Carine Pivoteau (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

We give a probabilistic analysis of parameters related to $\alpha$-gapped repeats and palindromes in random words, under both uniform and memoryless distributions (where letters have different probabilities, but are drawn independently). More precisely, we study the expected number of maximal $\alpha$-gapped patterns, as well as the expected length of the longest $\alpha$-gapped pattern in a random word.

Mots clés: analytic combinatorics; combinatorics on words; α-gapped repeats; random words; memoryless sources

Domaines: Informatique [cs]; Mathématique discrète [cs.DM]

Philippe Duchon, Cyril Nicaud, Carine Pivoteau. Gapped Pattern Statistics. 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017), Jul 2017, Varsovie, Poland. pp.21:1-21:12, ⟨10.4230/LIPIcs.CPM.2017.21⟩. ⟨hal-01565941⟩