Related papers: On friendship and cyclic parking functions
We show how to derive new instances of the cyclic sieving phenomenon from old ones via elementary representation theory. Examples are given involving objects such as words, parking functions, finite fields, and graphs.
We present here two examples of stochastic modelings of social phenomena. The first topic is pedestrian counter flow. Two groups of model pedestrians move in opposite directions and create congestions. It will be shown that this congestion…
An $(m, n)$-parking function can be characterized as function $f:[n] \to [m]$ such that the partition obtained by reordering the values of $f$ fits inside a right triangle with legs of length $m$ and $n$. Recent work by McCammond, Thomas,…
A parking function is a sequence of N nonnegative integers majorated by a permutation of the set {0, ..., N-1}. We provide a way to encode parking functions by data suggested by J.Haglund and N.Loehr. This coding is compared with another…
Traffic congestion has large economic and social costs. The introduction of autonomous vehicles can potentially reduce this congestion by increasing road capacity via vehicle platooning and by creating an avenue for influencing people's…
The classical house allocation problem involves assigning $n$ houses (or items) to $n$ agents according to their preferences. A key criterion in such problems is satisfying some fairness constraints such as envy-freeness. We consider a…
In many social dilemmas, individuals tend to generate a situation with low payoffs instead of a system optimum ("tragedy of the commons"). Is the routing of traffic a similar problem? In order to address this question, we present…
The problem of path planning for automated parking is usually presented as finding a collision-free path from initial to goal positions, where three out of four parking slot edges represent obstacles. We rethink the path planning problem…
This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction…
In this paper, we study temporal graphs arising from mobility models, where vertices correspond to agents moving in space and edges appear each time two agents meet. We propose a rather natural one-dimensional model. If each pair of agents…
We introduce type C parking functions, encoded as vertically labelled lattice paths and endowed with a statistic dinv'. We define a bijection from type C parking functions to regions of the Shi arrangement of type C, encoded as diagonally…
In recent years, we have witnessed a remarkable surge of usage in shared vehicles in our cities. Shared mobility offers a future of no congestion in busy city roads with increasing populations of travelers, passengers, and drivers. Given…
In the Seat Arrangement problem the goal is to allocate agents to vertices in a graph such that the resulting arrangement is optimal or fair in some way. Examples include an arrangement that maximises utility or one where no agent envies…
No human drives a car in a vacuum; she/he must negotiate with other road users to achieve their goals in social traffic scenes. A rational human driver can interact with other road users in a socially-compatible way through implicit…
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.…
With the increasing availability of transaction data collected by digital parking meters, paid curbside parking can be advantageously modeled as a network of interdependent queues. In this article we introduce methods for analyzing a…
While carpooling is widely adopted for long travels, it is by construction inefficient for daily commuting, where it is difficult to match drivers and riders, sharing similar origin, destination and time. To overcome this limitation, we…
In a given scenario, simultaneously and accurately predicting every possible interaction of traffic participants is an important capability for autonomous vehicles. The majority of current researches focused on the prediction of an single…
There is a tragedy of the traffic analogous to the tragedy of the commons that can be caused by overtaking. We analyze the effect of overtaking in a minimal model of vehicular traffic, the model proposed by Nagel and Schreckenberg, with two…
We recall the occupancy problem introduced by Konheim & Weiss in 1966 and we consider parking functions as hash maps. Each car $c_i$ prefers parking space $p_i$ (the hash map $c_i \mapsto p_i$ with $c_i$ is a key and $p_i$ an index into an…