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Pattern avoidance in parking functions [PDF]
Enumerative Combinatorics and Applications, 2023 In this paper, we view parking functions viewed as labeled Dyck paths in order to study a notion of pattern avoidance first introduced by Remmel and Qiu. In particular we enumerate the parking functions avoiding any set of two or more patterns of length 3, and we obtain a number of well-known combinatorial sequences as a result.
Ayomikun Adeniran, Lara Pudwell
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Improved Immune Moth–Flame Algorithm for Intelligent Vehicle Parking Path Optimization [PDF]
BiomimeticsIntelligent parking systems have been recognized as a core technological intervention for resolving parking garage shortages and advancing traffic safety. Nevertheless, it remains challenging to generate a smooth, accurate, and optimal parking trajectory
Yan Chen +3 more
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Parking functions for mappings
Journal of Combinatorial Theory - Series A, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marie-Louise Lackner, Alois Panholzer
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A further correspondence between $(bc,\bar{b})$-parking functions and $(bc,\bar{b})$-forests [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 For a fixed sequence of $n$ positive integers $(a,\bar{b}) := (a, b, b,\ldots, b)$, an $(a,\bar{b})$-parking function of length $n$ is a sequence $(p_1, p_2, \ldots, p_n)$ of positive integers whose nondecreasing rearrangement $q_1 \leq q_2 \leq \cdots ...
Heesung Shin, Jiang Zeng
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Vector parking functions with periodic boundaries and rational parking functions
Journal of Combinatorial Theory - Series A, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Catherine H Yan
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Parking functions and Łukasiewicz paths [PDF]
Discrete Mathematics LettersWe 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.
Thomas Selig, Haoyue Zhu
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Parking Functions and Descent Algebras [PDF]
Annals of Combinatorics, 2007 We show that the notion of parkization of a word, a variant of the classical standardization, allows to introduce an internal product on the Hopf algebra of parking functions. Its Catalan subalgebra is stable under this operation and contains the descent algebra as a left ideal.
Jean-Christophe Novelli +2 more
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Prime parking functions on rooted trees [PDF]
Journal of Combinatorial Theory - Series A, 2019 For a labeled, rooted tree with edges oriented towards the root, we consider the vertices as parking spots and the edge orientation as a one-way street. Each driver, starting with her preferred parking spot, searches for and parks in the first unoccupied spot along the directed path to the root. If all $n$ drivers park, the sequence of spot preferences
Catherine H Yan
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Enumeration of (p,q)-parking functions
Discrete Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Robert Cori
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The American Journal of CombinatoricsWe introduce a generalization of parking functions in which cars are limited in their movement backwards and forwards by two nonnegative integer parameters \(k\) and \(\ell\), respectively.
Jennifer Elder +5 more
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