Universal cycles for permutations

Details Universal cycles for permutations Universal cycles for permutations

2007-10-30

arxiv.org/abs/0710.5611v1

Mathematics

Combinatorics

14 pages, 2 figures

Scientific paper

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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