Omnibus Sequences, Coupon Collection, and Missing Word Counts
Sunil Abraham, Greg Brockman, Stephanie Sapp, Anant P. Godbole

TL;DR
This paper investigates Omnibus Sequences, which contain all possible messages of a certain length as subsequences, exploring their properties and connections to the coupon collector problem.
Contribution
It introduces and analyzes properties of Omnibus Sequences, linking them to classical coupon collector theory, and explores their combinatorial and probabilistic aspects.
Findings
Characterization of Omnibus Sequences
Connections established with coupon collector problem
Insights into missing word counts
Abstract
An {\it Omnibus Sequence} of length is one that has each possible "message" of length embedded in it as a subsequence. We study various properties of Omnibus Sequences in this paper, making connections, whenever possible, to the classical coupon collector problem.
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