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On the Monotonicity of the String Correction Factor for Words with Mismatches Apostolico, Alberto Pizzi, Cinzia Pattern discovery Motif Over-represented word Monotone score Correction Factor The string correction factor is the term by which the probability of a word $w$ needs to be multiplied in order to account for character changes or ``errors'' occurring in at most $k$ arbitrary positions in that word. The behavior of this factor, as a function of $k$ and of the word length, has implications on the number of candidates that need to be considered and weighted when looking for subwords of a sequence that present unusually recurrent replicas within some bounded number of mismatches. Specifically, it is seen that over intervals of mono- or bi-tonicity for the correction factor, only some of the candidates need be considered. This mitigates the computation and leads to tables of over-represented words that are more compact to represent and inspect. In recent work, expectation and score monotonicity has been established for a number of cases of interest, under {em i.i.d.} probabilistic assumptions. The present paper reviews the cases of bi-tonic behavior for the correction factor, concentrating on the instance in which the question is still open. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alberto Apostolico and Cinzia Pizzi 2006 Is Part Of Dagstuhl Seminar Proceedings, Volume 6201, Combinatorial and Algorithmic Foundations of Pattern and Association Discovery (2006) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.06201.5 urn:nbn:de:0030-drops-7899 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06201.5 eng https://creativecommons.org/licenses/by/4.0/legalcode