Results 41 to 50 of about 297,062 (318)
Parking Functions and Descent Algebras [PDF]
Annals of Combinatorics, 2007 We show that the notion of parkization of a word, a variant of the classical standardization, allows to introduce an internal product on the Hopf algebra of parking functions. Its Catalan subalgebra is stable under this operation and contains the descent algebra as a left ideal.
Novelli, Jean-Christophe +1 more
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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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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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The impact of ride hailing on parking (and vice versa)
Journal of Transport and Land Use, 2019 Investigating emerging transportation services is critical to forecasting mode choice and providing appropriate infrastructure. One such infrastructure is parking, as parking demand may shift with the availability of ride-hailing services.
Alejandro Henao, Wesley E. Marshall
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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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Reinforcement Learning-Based Motion Planning for Automatic Parking System
IEEE Access, 2020 In automatic parking motion planning, multi-objective optimization including safety, comfort, parking efficiency, and final parking performance should be considered.
Jiren Zhang +3 more
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IoT based smart parking model using Arduino UNO with FCFS priority scheduling
Measurement: Sensors, 2022 Develop a suitable method to handle parking problem in the crowded big city, as per the demand and number of parking slots available, by giving priority to the users with help of smart parking system.
M.R.M. Veeramanickam +5 more
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Some aspects of (r,k)-parking functions
, 2018 An \emph{$(r,k)$-parking function} of length $n$ may be defined as a sequence $(a_1,\dots,a_n)$ of positive integers whose increasing rearrangement $b_1\leq\cdots\leq b_n$ satisfies $b_i\leq k+(i-1)r$.
Stanley, Richard, Wang, Yinghui
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The monomial basis and the $Q$-basis of the Hopf algebra of parking functions
, 2015 Consider the vector space $\mathbb{K}\mathcal{P}$ spanned by parking functions. By representing parking functions as labeled digraphs, Hivert, Novelli and Thibon constructed a cocommutative Hopf algebra PQSym$^{*}$ on $\mathbb{K}\mathcal{P}$. The product
Li, Teresa Xueshan
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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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