Related papers: Counting Parking Sequences and Parking Assortments…
We determine the distributions of lengths of runs in random sequences of elements from a totally ordered set (total order) or partially ordered set (partial order). In particular, we produce novel formulae for the expected value, variance,…
How do we estimate the probability of an abundant objects' formation, with minimal context or assumption about is origin? To explore this we have previously introduced the concept of pathway assembly (as pathway complexity), in a graph…
We enumerate interlaced pairs of parking functions whose underlying Dyck path has a bounded height. We obtain an explicit formula for this enumeration in the form of a quotient of analogs of Chebicheff polynomials having coefficients in the…
The parking issue is central in transport policies and drivers' concerns, but the determinants of the parking search time remain relatively poorly understood. The question is often handled in a fairly ad hoc way, or by resorting to crude…
A permutation $\sigma$ describing the relative orders of the first $n$ iterates of a point $x$ under a self-map $f$ of the interval $I=[0,1]$ is called an \emph{order pattern}. For fixed $f$ and $n$, measuring the points $x\in I$ (according…
A pair $(G,K)$ of a group and its subgroup is called a Gelfand pair if the induced trivial representation of $K$ on $G$ is multiplicity free. Let $(a_j)$ be a sequence of positive integers of length $n$, and let $(b_i)$ be its…
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…
A data store allows application processes to put and get data from a shared memory. In general, a data store cannot be modelled as a strictly sequential process. Applications observe non-sequential behaviours, called anomalies. The set of…
The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the…
Parking spaces are resources that can be pooled together and shared, especially when there are complementary day-time and night-time users. We answer two design questions. First, given a quality of service requirement, how many spaces…
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
Planning in public transportation is traditionally done in a sequential process: After the network design process, the lines and their frequencies are planned. When these are fixed, a timetable is determined and based on the timetable, the…
This article proposes two different approaches to automatically create a map for valid on-street car parking spaces. For this, we use car sharing park-out events data. The first one uses spatial aggregation and the second a machine learning…
A composition of a nonnegative integer (n) is a sequence of positive integers whose sum is (n). A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of…
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…
This article introduces an adaptive sorting algorithm that can relocate elements accurately by substituting their values into a function which we name it the guessing function. We focus on building this function which is the mapping…
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.…
In prioritized planning for vehicles, vehicles plan trajectories in parallel or in sequence. Parallel prioritized planning offers approximately consistent computation time regardless of the number of vehicles but struggles to guarantee…
We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are…
We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to…