Related papers: Lehmer Parking Functions and Their Outcomes
In a scenario of growing usage of park-and-ride facilities, understanding and predicting car park occupancy is becoming increasingly important. This study presents a model that effectively captures the occupancy patterns of park-and-ride…
Let S be a set of states of a physical system and p(s) be the probability of the occurrence of an event when the system is in state s. A function p from S to [0,1] is called a numerical event or alternatively an S-probability. If a set…
We present a queuing model of parking dynamics and a model-based prediction method to provide real-time probabilistic forecasts of future parking occupancy. The queuing model has a non-homogeneous arrival rate and time-varying service time…
The Lerche-Newberger formula simplifies harmonic sums of Bessel functions and has seen application in plasma physics and frequency modulated quantum systems. In this paper, we rigorously prove the formula and extend the classical result to…
Parking has been a painful problem for urban drivers. The parking pain exacerbates as more people tend to live in cities in the context of global urbanization. Thus, it is demanding to find a solution to mitigate d rivers' parking…
We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $\beta$. We prove that if $\beta$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $\beta$…
We generalize a result of Garvan on inequalities and interpretations of the moments of the partition rank and crank functions. In particular for nearly 30 Bailey pairs, we introduce a rank-like function, establish inequalities with the…
We present Euler-type recurrence relations for some partition functions. Some of our results provide new recurrences for the number of unrestricted partitions of $n$, denote by $p(n)$. Others establish recurrences for partition functions…
In this paper, we will introduce Bell numbers $D(n)$ of type $D$ as an analogue to the classical Bell numbers related to all the partitions of the set $[n]$. Then based on a signed set partition of type $D$, we will construct the recurrence…
This paper studies partitions in the space of antimonotonic boolean functions on sets of n elements. The antimonotonic functions are the antichains of the partially ordered set of subsets. We analyse and characterise a natural partial…
We provide operadic interpretations for two Hopf subalgebras of the algebra of parking functions. The Catalan subalgebra is identified with the free duplicial algebra on one generator, and the Schr\"oder subalgebra is interpreted by means…
We provide a framework for Bell inequalities which is based on multilinear contractions. The derivation of the inequalities allows for an intuitive geometric depiction and their violation within quantum mechanics can be seen as a direct…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
The detection of nonlocal correlations in a Bell experiment implies almost by definition some intrinsic randomness in the measurement outcomes. For given correlations, or for a given Bell violation, the amount of randomness predicted by…
Parking functions are well researched and interesting results are found in the listed references and more. Some introductory results stemming from application to degree sequences of simple connected graphs are provided in this paper.…
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that…
Searching for a parking spot can waste time and gasoline. This waste can be reduced by assigning drivers to parking lots based on their destination and arrival time. In such a system, drivers could request a parking spot in advance and be…
We propose a generalized car parking problem where either a car of size $\sigma$ or of size $m\sigma$ ($m>1$) is sequentially parked on a line with probability $q$ and $(1-q)$, respectively. The free parameter $q$ interpolates between the…