Related papers: Subset Parking Functions
Having a function $f$ and a set of functionals $\{\mathcal{C}_{n}\}$, $c_n^f \equiv \mathcal{C}_n \left(f\right)$, one can interpret function approximation very generally as a construction of some function $\mathcal{A}_{N}^{f}$ such that…
Recently, the authors extended the notion of parking functions to parking sequences, which include cars of different sizes, and proved a product formula for the number of such sequences. We here give a refinement of that result involving…
Parking spots are essential components, providing vital mobile resources for residents in a city. Accurate Global Positioning System (GPS) points of parking spots are the core data for subsequent applications,e.g., parking management,…
Parking accurately and safely in highly constrained spaces remains a critical challenge. Unlike structured driving environments, parking requires executing complex maneuvers such as frequent gear shifts and steering saturation. Recent…
As the industry of autonomous driving grows, so does the potential interaction of groups of autonomous cars. Combined with the advancement of Artificial Intelligence and simulation, such groups can be simulated, and safety-critical models…
Parking guidance systems have recently become a popular trend as a part of the smart cities' paradigm of development. The crucial part of such systems is the algorithm allowing drivers to search for available parking lots across regions of…
We settle a conjecture of B\'ona regarding the log-concavity of a certain statistic on parking functions by utilizing recent log-concavity results on matroids. This result allows us to also prove that connected, labeled graphs graded by…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
Designing efficient car parking mechanisms that can be potentially integrated into future intelligent transportation systems is of crucial importance. Usually, the related design problems are combinatorial and the worst-case complexity of…
Real-time monitoring of traffic density, road congestion, public transportation, and parking availability are key to realizing the vision of a smarter city and, with the advent of vehicular networking technologies such as IEEE 802.11p and…
Four functions counting the number of subsets of $\{1, 2, ..., n\}$ having particular properties are defined by Nathanson and generalized by many authors. They derive explicit formulas for all four functions. In this paper, we point out…
With growing, Car parking increases with the number of car users. With the increased use of smartphones and their applications, users prefer mobile phone-based solutions. This paper proposes the Smart Parking Management System (SPMS) that…
We introduce a rather natural family of non-uniform distributions on $PF_n$, $n\in\mathbb{N}$, the set of parking functions of length $n$. One of the motivations for this comes from a similar situation in the context of integer partitions.…
For a class C of operations on a nonempty base set A, an operation f is called a C-subfunction of an operation g, if f = g(h_1, ..., h_n), where all the inner functions h_i are members of C. Two operations are C-equivalent if they are…
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…
We study lucky cars in subsets of parking functions, called Fubini rankings and unit Fubini rankings. A Fubini ranking is a sequence of nonnegative integers that encodes a valid ranking of competitors, where ties are allowed. A car (or…
We introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we a series of representations…
Parking guidance information (PGI) systems are used to provide information to drivers about the nearest parking lots and the number of vacant parking slots. Recently, vision-based solutions started to appear as a cost-effective alternative…
Autonomous valet parking is a specific application for autonomous vehicles. In this task, vehicles need to navigate in narrow, crowded and GPS-denied parking lots. Accurate localization ability is of great importance. Traditional…
We study Schroder paths drawn in a (m,n) rectangle, for any positive integers m and n. We get explicit enumeration formulas, closely linked to those for the corresponding (m,n)-Dyck paths. Moreover we study a Schroder version of…