Containing All Permutations

Numerous versions of the question "what is the shortest object containing all permutations of a given length?" have been asked over the past fifty years: by Karp (via Knuth) in 1972; by Chung, Diaconis, and Graham in 1992; by Ashlock and Tillotson in 1993; and by Arratia in 1999. The large...

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Bibliographic Details
Published inThe American mathematical monthly Vol. 128; no. 1; pp. 4 - 24
Main Authors Engen, Michael, Vatter, Vincent
Format Journal Article
LanguageEnglish
Published Washington Taylor & Francis 29.12.2020
Taylor & Francis Ltd
Subjects
Archives & records
Mathematical problems
MSC: Primary 05A05
Permutations
Polls & surveys
Questions
Secondary 68R15
Upper bounds
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Summary:Numerous versions of the question "what is the shortest object containing all permutations of a given length?" have been asked over the past fifty years: by Karp (via Knuth) in 1972; by Chung, Diaconis, and Graham in 1992; by Ashlock and Tillotson in 1993; and by Arratia in 1999. The large variety of questions of this form, which have previously been considered in isolation, stands in stark contrast to the dearth of answers. We survey and synthesize these questions and their partial answers, introduce infinitely more related questions, and then establish an improved upper bound for one of these questions.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2021.1835384