Results 11 to 20 of about 297,062 (318)
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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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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On Flattened Parking Functions [PDF]
, 2022 34 pages, two tables, appeared in the Journal of Integer ...
Jennifer Elder +4 more
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Some Properties of the Parking Function Poset [PDF]
The Electronic Journal of Combinatorics, 2022 In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his definition is a precursor of the parking space theory, in the framework of finite reflection groups. We present some enumerative and topological properties of this poset.
Bérénice Delcroix-Oger +2 more
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Tutte polynomial and G-parking functions [PDF]
Advances in Applied Mathematics, 2008 Let $G$ be a connected graph with vertex set $\{0,1,2,...,n\}$. We allow $G$ to have multiple edges and loops. In this paper, we give a characterization of external activity by some parameters of $G$-parking functions. In particular, we give the definition of the bridge vertex of a $G$-parking function and obtain an expression of the Tutte polynomial ...
Hungyung Chang, Jun Ma, Yeong‐Nan Yeh
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Generalizing Parking Functions with Randomness [PDF]
The Electronic Journal of Combinatorics, 2022 Consider $n$ cars $C_1, C_2, \ldots, C_n$ that want to park in a parking lot with parking spaces $1,2,\ldots,n$ that appear in order. Each car $C_i$ has a parking preference $\alpha_i \in \{1,2,\ldots,n\}$. The cars appear in order, if their preferred parking spot is not taken, they take it, if the parking spot is taken, they move forward until they ...
Melanie Tian, Enrique Treviño
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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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Primeness of generalized parking functions [PDF]
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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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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Orientations, Semiorders, Arrangements, and Parking Functions [PDF]
The Electronic Journal of Combinatorics, 2012 It is known that the Pak-Stanley labeling of the Shi hyperplane arrangement provides a bijection between the regions of the arrangement and parking functions. For any graph $G$, we define the $G$-semiorder arrangement and show that the Pak-Stanley labeling of its regions produces all $G$-parking functions.
Sam Hopkins, David Perkinson
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