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Discrete Mathematics Letters
Article . 2024 . Peer-reviewed
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Preprint . 2024
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Discrete Mathematics Letters
Article . 2024
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https://dx.doi.org/10.48550/ar...
Article . 2024
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Parking functions and Łukasiewicz paths

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 06 Nov 2024Embargo end date: 01 Jan 2024 English Publisher:Shahin Digital PublisherJournal:Discrete Mathematics Letters, volume 14, pages 77-84 (eissn: 2664-2557, Copyright policy )
Authors: Thomas Selig; Haoyue Zhu;

doi: 10.47443/dml.2024.070 , 10.48550/arxiv.2403.17438

arXiv: 2403.17438

Parking functions and Łukasiewicz paths

Abstract

We present a bijection between two well-known objects in the ubiquitous Catalan family: non-decreasing parking functions and Łukasiewicz paths. This bijection maps the maximal displacement of a parking function to the height of the corresponding Łukasiewicz path, and the total displacement to the area of the path. We also study this bijection restricted to two specific families of parking-functions: unit-interval parking functions, and prime parking functions.

11 pages, 5 figures. Comments welcome!

Related Organizations
Keywords

Permutations, words, matrices, 05A19 (Primary) 05A05, 05A10 (Secondary), Exact enumeration problems, generating functions, catalan numbers, Łukasiewicz paths, lukasiewicz paths, bijection, displacement statistic, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), parking functions, Catalan numbers, Factorials, binomial coefficients, combinatorial functions, Mathematics, Combinatorial identities, bijective combinatorics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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