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

Abstract

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.

Mathematics Subject Classification (2020):

• 05A16
• 05A05
• 60C05

Key words:

• Geometric random variable
• left-to-right maxima