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Bigraphical arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson.
Sam Hopkins, David Perkinson
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Parking Functions and Noncrossing Partitions [PDF]
The Electronic Journal of Combinatorics, 1996 A parking function is a sequence $(a_1,\dots,a_n)$ of positive integers such that, if $b_1\leq b_2\leq \cdots\leq b_n$ is the increasing rearrangement of the sequence $(a_1,\dots, a_n),$ then $b_i\leq i$. A noncrossing partition of the set $[n]=\{1,2,\dots,n\}$ is a partition $\pi$ of the set $[n]$ with the property that if $a < b < c < d ...
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Vacillating Parking Functions and the Fibonacci Numbers
The American Journal of CombinatoricsVacillating parking functions are parking functions in which a car only tolerates parking in its preferred spot, in the spot behind its preferred spot, or in the spot ahead of its preferred spot, which they check precisely in that order. Our main result
Pamela Harris
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Connecting $k$-Naples Parking Functions and Obstructed Parking Functions via Involutions
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.
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Optimization of intercept parking lots [PDF]
E3S Web of Conferences, 2020 The paper discusses the main prerequisites for the development of parking lots. The main problems are estimated, the solution of which is the construction of multi-level intercept parking lots. The urgency of the problem is associated with the increasing
Simankina Tatyana +2 more
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J. Integer Seq., 2019 A parking function $(c_1,\ldots,c_n)$ can be viewed as having $n$ cars trying to park on a one-way street with $n$ parking spots, where car $i$ tries to park in spot $c_i$, and otherwise he parks in the leftmost available spot after $c_i$. Another way to view this is that each car has a set $C_i$ of "acceptable" parking spots, namely $C_i=[c_i,n]$, and
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IEEE Open Journal of Vehicular TechnologyAutomated Vehicle Marshalling (AVM) is an innovative technology poised to transform the automotive industry by enabling automated vehicles to be wirelessly controlled within geofenced areas while ensuring guaranteed Functional Safety (FuSa).
F. A. Schiegg +16 more
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Journal of Advanced Transportation, 2020 For travelers who inevitably use motor vehicles, in the case of limited parking spaces, reserving parking spaces in destination in advance helps reduce the time and emissions of searching for parking spaces and alleviate road traffic pressure.
Yunqiang Xue +4 more
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From parking functions to Gelfand pairs [PDF]
Proceedings of the American Mathematical Society, 2011 A pair ( G , K ) (G,K)
Aker, Kursat, Can, Mahir Bilen
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Parking functions: interdisciplinary connections
Advances in Applied Probability, 2023 AbstractSuppose that m drivers each choose a preferred parking space in a linear car park with n spots. In order, each driver goes to their chosen spot and parks there if possible, and otherwise takes the next available spot if it exists. If all drivers park successfully, the sequence of choices is called a parking function. Classical parking functions
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