String overlaps, pattern matching, and nontransitive games

L. J. Guibas, A. M. Odlyzko

Research output: Contribution to journalArticlepeer-review

235 Scopus citations


This paper studies several topics concerning the way strings can overlap. The key notion of the correlation of two strings is introduced, which is a representation of how the second string can overlap into the first. This notion is then used to state and prove a formula for the generating function that enumerates the q-ary strings of length n which contain none of a given finite set of patterns. Various generalizations of this basic result are also discussed. This formula is next used to study a wide variety of seemingly unrelated problems. The first application is to the nontransitive dominance relations arising out of a probabilistic coin-tossing game. Another application shows that no algorithm can check for the presence of a given pattern in a text without examining essentially all characters of the text in the worst case. Finally, a class of polynomials arising in connection with the main result are shown to be irreducible.

Original languageEnglish (US)
Pages (from-to)183-208
Number of pages26
JournalJournal of Combinatorial Theory, Series A
Issue number2
StatePublished - Mar 1981


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