Related papers: Subset Parking Functions
For each skew shape we define a nonhomogeneous symmetric function, generalizing a construction of Pak and Postnikov. In two special cases, we show that the coefficients of this function when expanded in the complete homogeneous basis are…
Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each…
Vehicle-sharing systems are becoming important for urban transportation. In these systems, users arrive at a station, pick up a vehicle, use it for a while and then return it to another station of their choice. Depending on the type of…
For any irreducible real reflection group $W$ with Coxeter number $h$, Armstrong, Reiner, and the author introduced a pair of $W \times \ZZ_h$-modules which deserve to be called {\sf $W$-parking spaces} which generalize the type A notion of…
In recent years, innovative roadside parking vacancy crowdsensing solutions have emerged as a cost-effective alternative to traditional methods, which can significantly reduce sensor installation and maintenance expenses. This crowdsensing…
Recent results have placed the classical shuffle conjecture of Haglund et al. in a broader context of an infinite family of conjectures about parking functions in any rectangular lattice. The combinatorial side of the new conjectures has…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
In this paper, we develop a method to detect vacant parking spaces in an environment with unclear segments and contours with the help of MATLAB image processing capabilities. Due to the anomalies present in the parking spaces, such as…
Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
Our paper approaches the parking assistance service in urban environments as an instance of service provision in non-cooperative network environments. We propose normative abstractions for the way drivers pursue parking space and the way…
On-street parking is convenient, but has many disadvantages: on-street spots come at the expense of other road uses such as traffic lanes, transit lanes, bike lanes, or parklets; drivers looking for parking contribute substantially to…
The problem of autonomous parking of vehicle fleets is addressed in this paper. We present a system-level modeling and control framework which allows investigating different vehicle parking strategies while taking into account path planning…
In this expository article I describe classical results in the combinatorics of parking functions. Its English-Spanish translation is included. -- -- En este art\'iculo de difusi\'on matem\'atica describo resultados cl\'asicos en la…
Street parking spots for automobiles are a scarce commodity in most urban environments. The heterogeneity of car sizes makes it inefficient to rigidly define fixed-sized spots. Instead, unmarked streets in cities like New York leave…
Park-and-ride facilities are car parks where users can transfer to public transportation. Commuters can use P&R facilities or choose to travel by car to their destinations, and individual choice behavior is assumed to follow a logit model.…
We study the problem of multiset prediction. The goal of multiset prediction is to train a predictor that maps an input to a multiset consisting of multiple items. Unlike existing problems in supervised learning, such as classification,…
We extend the notion of parking function polytopes and study their geometric and combinatorial structure, including normal fans, face posets, and $h$-polynomials, as well as their connections to other classes of polytopes. To capture their…
Occupied truck parking lots regularly cause hazardous situations. Estimation of current parking lot state could be utilized to provide drivers parking recommendations. In this work, we highlight based on a simulation scenario, how sparse…
Autonomous parking technology is a key concept within autonomous driving research. This paper will propose an imaginative autonomous parking algorithm to solve issues concerned with parking. The proposed algorithm consists of three parts:…