## Biers-Ariel, Yonah and Godbole, Anant and Kelley, Elizabeth - Expected Number of Distinct Subsequences in Randomly Generated Binary Strings

dmtcs:3287 - Discrete Mathematics & Theoretical Computer Science, June 26, 2018, Vol. 19 no. 2, Permutation Patterns 2016
Expected Number of Distinct Subsequences in Randomly Generated Binary Strings

Authors: Biers-Ariel, Yonah and Godbole, Anant and Kelley, Elizabeth

When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct subsequences in a fixed string, we might next be interested in the expected number of distinct subsequences in random strings. This expected value is already known for random binary strings where each letter in the string is, independently, equally likely to be a 1 or a 0. We generalize this result to random strings where the letter 1 appears independently with probability $\alpha \in [0,1]$. Also, we make some progress in the case of random strings from an arbitrary alphabet as well as when the string is generated by a two-state Markov chain.

Source : oai:arXiv.org:1704.08661
DOI : 10.23638/DMTCS-19-2-10
Volume: Vol. 19 no. 2, Permutation Patterns 2016
Section: Permutation Patterns
Published on: June 26, 2018
Submitted on: April 28, 2017
Keywords: Mathematics - Combinatorics,05D40, 60C05