Products of Universal Cycles

2008 ◽  
pp. 35-55 ◽  
Author(s):  
Persi Diaconis ◽  
Ron Graham
Keyword(s):  
Universal Cycles

scholarly journals Universal Cycles for Weak Orders

2013 ◽  
Vol 27 (3) ◽  
pp. 1360-1371 ◽  
Author(s):  
Victoria Horan ◽  
Glenn Hurlbert
Keyword(s):  
Universal Cycles ◽  
Weak Orders

Shorthand Universal Cycles for Permutations

Algorithmica ◽  
2011 ◽  
Vol 64 (2) ◽  
pp. 215-245 ◽  
Author(s):  
Alexander E. Holroyd ◽  
Frank Ruskey ◽  
Aaron Williams
Keyword(s):  
Universal Cycles

scholarly journals Universal cycles of classes of restricted words

2010 ◽  
Vol 310 (23) ◽  
pp. 3303-3309 ◽  
Author(s):  
Arielle Leitner ◽  
Anant Godbole
Keyword(s):  
Universal Cycles

scholarly journals Universal cycles for permutation classes

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Michael Albert ◽  
Julian West
Keyword(s):  
General Result ◽  
Universal Cycles ◽  
Set Of Permutations ◽  
International Audience

International audience We define a universal cycle for a class of $n$-permutations as a cyclic word in which each element of the class occurs exactly once as an $n$-factor. We give a general result for cyclically closed classes, and then survey the situation when the class is defined as the avoidance class of a set of permutations of length $3$, or of a set of permutations of mixed lengths $3$ and $4$. Nous définissons un cycle universel pour une classe de $n$-permutations comme un mot cyclique dans lequel chaque élément de la classe apparaît une unique fois comme $n$-facteur. Nous donnons un résultat général pour les classes cycliquement closes, et détaillons la situation où la classe de permutations est définie par motifs exclus, avec des motifs de taille $3$, ou bien à la fois des motifs de taille $3$ et de taille $4$.

A Successor Rule Framework for Constructing $k$ -Ary de Bruijn Sequences and Universal Cycles

2020 ◽  
Vol 66 (1) ◽  
pp. 679-687 ◽  
Author(s):  
D. Gabric ◽  
J. Sawada ◽  
A. Williams ◽  
D. Wong
Keyword(s):  
Universal Cycles ◽  
De Bruijn Sequences ◽  
De Bruijn

scholarly journals On a Greedy Algorithm to Construct Universal Cycles for Permutations

2019 ◽  
Vol 30 (01) ◽  
pp. 61-72
Author(s):  
Alice L. L. Gao ◽  
Sergey Kitaev ◽  
Wolfgang Steiner ◽  
Philip B. Zhang
Keyword(s):  
Greedy Algorithm ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Universal Cycles

A universal cycle for permutations of length [Formula: see text] is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length [Formula: see text], and containing all permutations of length [Formula: see text] as factors. It is well known that universal cycles for permutations of length [Formula: see text] exist. However, all known ways to construct such cycles are rather complicated. For example, in the original paper establishing the existence of the universal cycles, constructing such a cycle involves finding an Eulerian cycle in a certain graph and then dealing with partially ordered sets. In this paper, we offer a simple way to generate a universal cycle for permutations of length [Formula: see text], which is based on applying a greedy algorithm to a permutation of length [Formula: see text]. We prove that this approach gives a unique universal cycle [Formula: see text] for permutations, and we study properties of [Formula: see text].

scholarly journals Universal cycles of k-subsets and k-permutations

1993 ◽  
Vol 117 (1-3) ◽  
pp. 141-150 ◽  
Author(s):  
B.W. Jackson
Keyword(s):  
Universal Cycles

scholarly journals Near-Universal Cycles for Subsets Exist

2009 ◽  
Vol 23 (3) ◽  
pp. 1441-1449 ◽  
Author(s):  
Dawn Curtis ◽  
Taylor Hines ◽  
Glenn Hurlbert ◽  
Tatiana Moyer
Keyword(s):  
Universal Cycles
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