Results 11 to 20 of about 2,802,612 (287)
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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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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Connecting $k$-Naples Parking Functions and Obstructed Parking Functions via Involutions [PDF]
The Electronic Journal of Combinatorics, 2022 Parking functions were classically defined for $n$ cars attempting to park on a one-way street with $n$ parking spots, where cars only drive forward. Subsequently, parking functions have been generalized in various ways, including allowing cars the option of driving backward.
Tian, Roger
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Primeness of Generalized Parking Functions
The Electronic Journal of CombinatoricsClassical parking functions are a generalization of permutations that appear in many combinatorial structures. Prime parking functions are indecomposable components such that any classical parking function can be uniquely described as a direct sum of prime ones.
Sam Armon +6 more
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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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Parking functions, valet functions and priority queues [PDF]
Discrete Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Julian D. Gilbey, Louis H. Kalikow
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Vacillating parking functions [PDF]
For any integers $1\leq k\leq n$, we introduce a new family of parking functions called $k$-vacillating parking functions of length $n$. The parking rule for $k$-vacillating parking functions allows a car with preference $p$ to park in the first available spot in encounters among the parking spots numbered $p$, $p-k$, and $p+k$ (in that order and if ...
Fang, Bruce +3 more
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Probabilistic Parking Functions
The Electronic Journal of Combinatorics, 2023 We consider the notion of classical parking functions by introducing randomness and a new parking protocol, as inspired by the work presented in the paper ``Parking Functions: Choose your own adventure,'' (arXiv:2001.04817) by Carlson, Christensen, Harris, Jones, and Rodríguez.
Irfan Durmic +4 more
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Advances in Applied Mathematics, 2021 Interval parking functions (IPFs) are a generalization of ordinary parking functions in which each car is willing to park only in a fixed interval of spaces. Each interval parking function can be expressed as a pair $(a,b)$, where $a$ is a parking function and $b$ is a dual parking function. We say that a pair of permutations $(x,y)$ is \emph{reachable}
Emma Colaric +3 more
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Partial parking functions [PDF]
Discrete Mathematics, 2019 11 pages.
Rui Duarte, António Guedes de Oliveira
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