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Universal cycles for permutations

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arxiv 0710.5611 v1 pith:POGEZSYO submitted 2007-10-30 math.CO

J. Robert Johnson This is my paper · ORCID
classification math.CO
keywords universalcycledistinctintegerspermutationspossiblewordbest
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A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1 distinct integers are used. This is best possible and proves a conjecture of Chung, Diaconis and Graham.

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  1. Superpermutation matrices

    math.CO 2019-08 conditional novelty 6.0 of 10

    Defines superpermutation matrices, reduces their row/column minimization to a universal word problem for quotient classes in S_n, and proves the ratio of the resulting upper and lower bounds tends to 2 as n grows.

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