The number of distinct adjacent pairs in geometrically distributed words
Date
2021-01-28
Journal Title
Journal ISSN
Volume Title
Publisher
Episciences.org
Abstract
A sequence of geometric random variables of length n is a sequence of n independent and identically distributed geometric random variables (Γ1,Γ2,…,Γn) where P(Γj=i)=pqi−1 for 1 ≤ j ≤ n with p+q=1. We study the number of distinct adjacent two letter patterns in such sequences. Initially we directly count the number of distinct pairs in words of short length. Because of the rapid growth of the number of word patterns we change our approach to this problem by obtaining an expression for the expected number of distinct pairs in words of length n. We also obtain the asymptotics for the expected number as n→∞.
Description
CITATION: Archibald, M. et al. 2021. The number of distinct adjacent pairs in geometrically distributed words. Discrete Mathematics & Theoretical Computer Science, 22(4) doi:10.23638/DMTCS-22-4-10
The original publication is available at https://dmtcs.episciences.org/
The original publication is available at https://dmtcs.episciences.org/
Keywords
Geometric random variables, Pairs, Generating functions, Asymptotics, Binary system (Mathematics)
Citation
Archibald, M. et al. 2021. The number of distinct adjacent pairs in geometrically distributed words. Discrete Mathematics & Theoretical Computer Science, 22(4) doi:10.23638/DMTCS-22-4-10