Related papers: On Increasing and Invariant Parking Sequences
Autonomous parking systems start with the detection of available parking slots. Parking slot detection performance has been dramatically improved by deep learning techniques. Deep learning-based object detection methods can be categorized…
We consider a system of ordered cars moving in $\R$ from right to left. Each car is represented by a point in $\R$; two or more cars can occupy the same point but cannot overpass. Cars have two possible velocities: either 0 or 1. An…
Sequences whose terms are equal to the number of functions with specified properties are considered. Properties are based on the notion of derangements in a more general sense. Several sequences which generalize the standard notion of…
In this paper, we explore parking distributions on caterpillar trees, focusing on two primary statistics: the number of lucky cars and the frequency with which cars prefer specific parking spaces. We use first-return decomposition to reveal…
An inversion sequence of length $n$ is an integer sequence $e=e_{1}e_{2}\dots e_{n}$ such that $0\leq e_{i}<i$ for each $i$. Corteel--Martinez--Savage--Weselcouch and Mansour--Shattuck began the study of patterns in inversion sequences,…
In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his definition is a precursor of the parking space theory, in the…
A method to apply and visualize persistent homology of time series is proposed. The method captures persistent features in space and time, in contrast to the existing procedures, where one usually chooses one while keeping the other fixed.…
An improvement in technology is linearly related to time and time-relevant problems. It has been seen that as time progresses, the number of problems humans face also increases. However, technology to resolve these problems tends to improve…
Autonomous parking is a crucial task in the intelligent driving field. Traditional parking algorithms are usually implemented using rule-based schemes. However, these methods are less effective in complex parking scenarios due to the…
In 1980, G. Kreweras gave a recursive bijection between forests and parking functions. In this paper we construct a nonrecursive bijection from forests onto parking functions, which answers a question raised by R. Stanley. As a by-product,…
An infinite real sequence $\{a_n\}$ is called an invariant sequence of the first (resp., second) kind if $a_n=\sum_{k=0}^n {n \choose k} (-1)^k a_k$ (resp., $a_n=\sum_{k=n}^{\infty} {k \choose n} (-1)^k a_k$). We review and investigate…
Illegal vehicle parking is a common urban problem faced by major cities in the world, as it incurs traffic jams, which lead to air pollution and traffic accidents. The government highly relies on active human efforts to detect illegal…
Tiered trees were introduced as a combinatorial object for counting absolutely indecomposable representation of certain quivers and torus orbit of certain homogeneous variety. In this paper, we define a bijection between the set of…
A sequence $(a_1, \ldots, a_n)$ of nonnegative integers is an {\em ascent sequence} if $a_0 =0$ and for all $i \geq 2$, $a_i$ is at most 1 plus the number of ascents in $(a_1, \ldots, a_{i-1})$. Ascent sequences were introduced by…
To provide real-time parking information, existing studies focus on predicting parking availability, which seems an indirect approach to saving drivers' cruising time. In this paper, we first time propose an on-street parking recommendation…
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…
Parking plays a central role in transport policies and has wide-ranging consequences: While the average time spent searching for parking exceeds dozens of hours per driver every year in many Western cities, the associated cruising traffic…
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…
Real-time parking occupancy information is valuable for guiding drivers' searching for parking spaces. Recently many parking detection systems using range-based on-vehicle sensors are invented, but they disregard the practical difficulty of…
The dominant approach to sequence generation is to produce a sequence in some predefined order, e.g. left to right. In contrast, we propose a more general model that can generate the output sequence by inserting tokens in any arbitrary…