What is it about?
Given a finite alphabet and a finite set of "dirty words", enumerating the number of n-letter words that are clean is well known, and can be done very efficiently using, for example, the so-called Goulden-Jackson cluster method, but counting how many n-letter clean words are there with k clean neighbors (in the sense of Hamming distance 1) is novel.
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Why is it important?
It speaks for itself
Perspectives
It generalizes a beautiful paper co-authored by my late friend and collaborator Marko Petkovsek, and is dedicated to his memory
Doron Zeilberger
Rutgers University New Brunswick
Read the Original
This page is a summary of: Counting Clean Words According to the Number of Their Clean Neighbors, ACM Communications in Computer Algebra, March 2023, ACM (Association for Computing Machinery),
DOI: 10.1145/3610377.3610379.
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