The Number of Distinct Subsequences of a Random Binary String

TL;DR

This paper analyzes the average number of distinct subsequences in random binary strings, providing estimates for subsequences of specific lengths, thereby advancing understanding of combinatorial properties of random sequences.

Contribution

It introduces new analytical methods to compute the expected number of distinct subsequences in random binary strings and estimates for subsequences of given lengths.

Findings

Derived formulas for average number of distinct subsequences

Estimated counts for subsequences of specific lengths

Enhanced understanding of binary string combinatorics

Abstract

We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.