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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2007
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0701488 |
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| _version_ | 1866913244536373248 |
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| author | Hurlbert, Glenn Johnson, Tobias Zahl, Joshua |
| author_facet | Hurlbert, Glenn Johnson, Tobias Zahl, Joshua |
| contents | A Universal Cycle for t-multisets of [n]={1,...,n} is a cyclic sequence of $\binom{n+t-1}{t}$ integers from [n] with the property that each t-multiset of [n] appears exactly once consecutively in the sequence. For such a sequence to exist it is necessary that n divides $\binom{n+t-1}{t}$, and it is reasonable to conjecture that this condition is sufficient for large enough n in terms of t. We prove the conjecture completely for t in {2,3} and partially for t in {4,6}. These results also support a positive answer to a question of Knuth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0701488 |
| institution | arXiv |
| publishDate | 2007 |
| record_format | arxiv |
| spellingShingle | On Universal Cycles for Multisets Hurlbert, Glenn Johnson, Tobias Zahl, Joshua Combinatorics 05B30 A Universal Cycle for t-multisets of [n]={1,...,n} is a cyclic sequence of $\binom{n+t-1}{t}$ integers from [n] with the property that each t-multiset of [n] appears exactly once consecutively in the sequence. For such a sequence to exist it is necessary that n divides $\binom{n+t-1}{t}$, and it is reasonable to conjecture that this condition is sufficient for large enough n in terms of t. We prove the conjecture completely for t in {2,3} and partially for t in {4,6}. These results also support a positive answer to a question of Knuth. |
| title | On Universal Cycles for Multisets |
| topic | Combinatorics 05B30 |
| url | https://arxiv.org/abs/math/0701488 |