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arXiv · 1703.08735

Roller Coaster Permutations and Partition Numbers

William Adamczak
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Abstract

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.

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William Adamczak. 2017-03-25. Roller Coaster Permutations and Partition Numbers. https://arxiv.org/abs/1703.08735

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