Roller Coaster Permutations and Partition Numbers
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866914224271261696 |
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| author | Adamczak, William |
| author_facet | Adamczak, William |
| contents | This paper explores the partition properties of roller coaster permutations, a class of permutations characterized by maximizing the number of alternating runs in all subsequences. We establish a connection between the structure of these permutations and their partition numbers, defined as the minimum number of monotonic subsequences required to cover the permutation. Our main result provides a theoretical upper bound for the partition number of a roller coaster permutation of length $n$, given by $P_{max}(n) \le \lfloor\frac{\lceil\frac{n-2}{2}\rceil}{2}\rfloor + 2$. We further present experimental data for $n < 15$ that suggests this bound is nearly sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_08735 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Roller Coaster Permutations and Partition Numbers Adamczak, William Combinatorics This paper explores the partition properties of roller coaster permutations, a class of permutations characterized by maximizing the number of alternating runs in all subsequences. We establish a connection between the structure of these permutations and their partition numbers, defined as the minimum number of monotonic subsequences required to cover the permutation. Our main result provides a theoretical upper bound for the partition number of a roller coaster permutation of length $n$, given by $P_{max}(n) \le \lfloor\frac{\lceil\frac{n-2}{2}\rceil}{2}\rfloor + 2$. We further present experimental data for $n < 15$ that suggests this bound is nearly sharp. |
| title | Roller Coaster Permutations and Partition Numbers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1703.08735 |