Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2007
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0701488 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.