Results 1 to 10 of about 13,101 (162)
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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Function Replacement Decision-Making for Parking Space Renewal Based on Association Rules Mining
Land, 2022 Parking lots are typical urban spaces with a large total area and scattered distribution. With the development of smart cars and shared driving, parking demand is likely to decline.
Bing Xia, Yichen Ruan
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Applied Sciences, 2021 To optimize performances such as continuous curvature, safety, and satisfying curvature constraints of the initial planning path for driverless vehicles in parallel parking, a novel method is proposed to train control points of the Bézier curve using the
Leiyan Yu +5 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 Hierarchical NMPC and TD3-Based Framework for Seamless Cruise-to-Park Automated Valet Parking [PDF]
SensorsAutomated valet parking requires reliable long-range slot searching and precise low-speed docking in confined structured lots. This paper proposes a hierarchical cruise-to-park framework that combines nonlinear model predictive control (NMPC) for ...
Dajie Tian, Levent Guvenc
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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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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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A Parking Function Setting for Nabla Images of Schur Functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In this article, we show how the compositional refinement of the ``Shuffle Conjecture'' due to Jim Haglund, Jennifer Morse, and Mike Zabrocki can be used to express the image of a Schur function under the Bergeron-Garsia Nabla operator as a weighted sum ...
Yeonkyung Kim
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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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Special Cases of the Parking Functions Conjecture and Upper-Triangular Matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We examine the $q=1$ and $t=0$ special cases of the parking functions conjecture. The parking functions conjecture states that the Hilbert series for the space of diagonal harmonics is equal to the bivariate generating function of $area$ and $dinv$ over ...
Paul Levande
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