Admissible Pinnacle Orderings

A pinnacle of a permutation is a value that is larger than its immediate neighbors when written in one-line notation. In this paper, we build on previous work that characterized admissible pinnacle sets of permutations. For these sets, there can be specific orderings of the pinnacles that are not ad...

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Bibliographic Details
Published in:Graphs and combinatorics 2021-07, Vol.37 (4), p.1205-1214
Main Authors: Rusu, Irena, Tenner, Bridget Eileen
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Engineering Design
Mathematics
Mathematics and Statistics
Original Paper
Peaks (landforms)
Permutations
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Summary:A pinnacle of a permutation is a value that is larger than its immediate neighbors when written in one-line notation. In this paper, we build on previous work that characterized admissible pinnacle sets of permutations. For these sets, there can be specific orderings of the pinnacles that are not admissible, meaning that they are not realized by any permutation. Here we characterize admissible orderings, using the relationship between a pinnacle x and its rank in the pinnacle set to bound the number of times that the pinnacles less than or equal to x can be interrupted by larger values.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-021-02306-9