Universal Cycles on 3-Multisets

dc.creatorJohnson, Tobias L.
dc.creatorZahl, Joshua
dc.date2006-08-30
dc.date.accessioned2026-07-07T07:22:21Z
dc.date.available2026-07-07T07:22:21Z
dc.descriptionConsider 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 and similar combinatorial structures was first addressed by DeBruijn in 1946 (who considered t-tuples instead of t-multisets). The past 15 years has seen a resurgence of interest in this area, primarily due to Chung, Diaconis, and Graham's 1992 paper on the subject. For the case t=3, we determine necessary and sufficient conditions on n for the existence of universal cycles, and we examine how this technique can be generalized to other values of t.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math/0608769
dc.identifierhttp://arxiv.org/abs/math/0608769
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115632
dc.subjectCombinatorics
dc.subject05B30
dc.titleUniversal Cycles on 3-Multisets
dc.typetext

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