The multiplicity of left-to-right maxima in geometrically distributed words

  • A. Knopfmacher
  • M. Archibald
Keywords: Geometric random variable, left-to-right maxima.


For fixed m ≥ 1, we study the number of weak left-to-right maxima which occur exactly m times in words whose letters satisfy a geometric distribution. First, we find the generating function and two exact expressions for the mean. Thereafter we use Rice's integrals to derive an asymptotic formula as n tends to infinity for the average in random geometric words of length n for each fixed value of m.


Journal Identifiers

eISSN: 1727-933X
print ISSN: 1607-3606