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arXiv · 2101.07081

Merging-Free Partitions and Run-Sorted Permutations

Fufa Beyene·Roberto Mantaci
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Abstract

In this paper, we study merging-free partitions with their canonical forms and run-sorted permutations. We give a combinatorial proof of the conjecture made by Nabawanda et al. We describe the distribution of the statistics of runs and right-to-left minima over the set of run-sorted permutations and we give the exponential generating function for their joint distribution. We show the number of right-to-left minima is given by the shifted distribution of the Stirling number of the second kind. We also prove that the non-crossing merging-free partitions are enumerated by powers of 2. We use one of the constructive proofs given in the paper to implement an algorithm for the exhaustive generation of run-sorted permutations by number of runs.

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Fufa Beyene, Roberto Mantaci. 2021-01-18. Merging-Free Partitions and Run-Sorted Permutations. https://arxiv.org/abs/2101.07081

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