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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This Isabelle/HOL formalization introduces a nested multiset datatype and de nes Dershowitz and Manna's nested multiset order. The order is proved well founded and linear. By removing one constructor, we transform the nested multisets into hereditary multisets. These are isomorphic to the syntactic ordinals the ordinals can be recursively expressed in Cantor normal form. Addition, subtraction, ...
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Multisets are now a common tool and a fundamental framework in information processing. Their generalization to fuzzy multisets has also been studied. In this paper the basics of multisets and fuzzy multisets are reviewed, fundamental properties of fuzzy multisets are proved, and advanced operations are defined. Applications to rough sets, fuzzy data retrieval, and automatic classification are m...
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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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ژورنال
عنوان ژورنال: SIAM Journal on Algebraic Discrete Methods
سال: 1982
ISSN: 0196-5212,2168-345X
DOI: 10.1137/0603037