Yonah Biers-Ariel ; Anant Godbole ; Elizabeth Kelley - 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 - https://doi.org/10.23638/DMTCS-19-2-10
Expected Number of Distinct Subsequences in Randomly Generated Binary Strings

Authors: Yonah Biers-Ariel ; Anant Godbole ; Elizabeth Kelley

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.

Volume: Vol. 19 no. 2, Permutation Patterns 2016
Section: Permutation Patterns
Published on: June 26, 2018
Accepted on: June 26, 2018
Submitted on: April 28, 2017
Keywords: Mathematics - Combinatorics,05D40, 60C05
Fundings :
Source : OpenAIRE Research Graph
• REU Site: Combinatorics and Probability; Funder: National Science Foundation; Code: 1263009