Universal Cycles on 3-Multisets
| dc.creator | Johnson, Tobias L. | |
| dc.creator | Zahl, Joshua | |
| dc.date | 2006-08-30 | |
| dc.date.accessioned | 2026-07-07T07:22:21Z | |
| dc.date.available | 2026-07-07T07:22:21Z | |
| dc.description | 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 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.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608769 | |
| dc.identifier | http://arxiv.org/abs/math/0608769 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115632 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B30 | |
| dc.title | Universal Cycles on 3-Multisets | |
| dc.type | text |