On universal cycles for multisets
نویسندگان
چکیده
منابع مشابه
On universal cycles for multisets
A Universal Cycle for t-multisets of [n] = {1, . . . , n} is a cyclic sequence of ( n+t−1 t ) integers from [n] with the property that each tmultiset of [n] appears exactly once consecutively in the sequence. For such a sequence to exist it is necessary that n divides ( n+t−1 t ) , and it is reasonable to conjecture that this condition is sufficient for large enough n in terms of t. We prove th...
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Consider the collection of all t–multisets of {1, . . . , n}. A universal cycle on multisets is a string of numbers, each of which is between 1 and n, such that if these numbers are considered in t–sized windows, every multiset in the collection is present in the string precisely once. The problem of finding necessary and sufficient conditions on n and t for the existence of universal cycles an...
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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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متن کاملUniversal Cycles for Weak Orders
Universal cycles are generalizations of de Bruijn cycles and Gray codes that were introduced originally by Chung, Diaconis, and Graham in 1992. They have been developed by many authors since, for various combinatorial objects such as strings, subsets, permutations, partitions, vector spaces, and designs. One generalization of universal cycles, which require almost complete overlap of consecutiv...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.04.050