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Generalizing Parking Functions with Randomness
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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The Number of Prime Parking Functions
The Mathematical Intelligencer, 2023 A parking function of length $n$ is prime if we obtain a parking function of length $n-1$ by deleting one 1 from it. In this note we give a new direct proof that the number of prime parking functions of length $n$ is $(n-1)^{n-1}$. This proof leads to a new interpretation, in close terms to the definition of parking function.
Duarte, Rui +1 more
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On Flattened Parking Functions
, 2022 34 pages, two tables, appeared in the Journal of Integer ...
Elder, Jennifer +4 more
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Counting Defective Parking Functions [PDF]
The Electronic Journal of Combinatorics, 2008 Suppose that $m$ drivers each choose a preferred parking space in a linear car park with $n$ spaces. Each driver goes to the chosen space and parks there if it is free, and otherwise takes the first available space with a larger number (if any). If all drivers park successfully, the sequence of choices is called a parking function.
Cameron, P. +3 more
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Multidimensional Parking Functions [PDF]
, 2023 Two multidimensional generalizations of Konheim and Weiss’ classical parking functions are the U -parking functions and the (p, q)-parking functions.
Snider, Lauren Leigh
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Extending the parking space [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The action of the symmetric group $S_n$ on the set $\mathrm{Park}_n$ of parking functions of size $n$ has received a great deal of attention in algebraic combinatorics.
Andrew Berget, Brendon Rhoades
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Transport Automation in Urban Mobility: A Case Study of an Autonomous Parking System
Vehicles, 2022 Parking road vehicles is one of the most tedious and challenging tasks a human driver performs. Despite the low speeds involved, parking manoeuvres are among the main causes of minor and sometimes major traffic accidents, especially in urban areas where ...
Jiri Plihal +4 more
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Probabilizing parking functions
Advances in Applied Mathematics, 2017 We explore the link between combinatorics and probability generated by the question "What does a random parking function look like?" This gives rise to novel probabilistic interpretations of some elegant, known generating functions. It leads to new combinatorics: how many parking functions begin with $i$?
Persi Diaconis, Angela Hicks
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An explicit formula for ndinv, a new statistic for two-shuffle parking functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In a recent paper, Duane, Garsia, and Zabrocki introduced a new statistic, "ndinv'', on a family of parking functions. The definition was guided by a recursion satisfied by the polynomial $\langle\Delta_{h_m}C_p1C_p2...C_{pk}1,e_n\rangle$, for $\Delta_ ...
Angela Hicks, Yeonkyung Kim
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From G-parking functions to B-parking functions [PDF]
Journal of Combinatorial Theory, Series A, 2018 A matching $M$ in a multigraph $G=(V,E)$ is said to be uniquely restricted if $M$ is the only perfect matching in the subgraph of $G$ induced by $V(M)$ (i.e., the set of vertices saturated by $M$). For any fixed vertex $x_0$ in $G$, there is a bijection from the set of spanning trees of $G$ to the set of uniquely restricted matchings of size $|V|-1$ in
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