Stefano Bilotta

• University of Florence

Given a positive rational $q$, we consider Dyck paths having height at most two with some constraints on the number of consecutive peaks and consecutive valleys, depending on $q$. We introduce a general class of Dyck paths, called rational Dyck paths, and provide the associated generating function, according to their semilength, as well as the cons...

Urban traffic congestion and pollution represent critical challenges for sustainable city development. In this paper, we presents a novel approach to optimizing urban mobility infrastructure using a stochastic relaxation algorithm. The method is designed to address the growing challenges of traffic congestion, fuel consumption, and CO2 emissions in...

We consider Dyck paths having height at most two with some constraints on the number of consecutive valleys at height one which must be followed by a suitable number of valleys at height zero. We prove that they are enumerated by so-called Q-bonacci numbers (recently introduced by Kirgizov) which generalize the classical q-bonacci numbers in the ca...

Due to increasing urbanization, nowadays, cities are facing challenges spanning multiple domains such as mobility, energy, environment, etc. For example, to reduce traffic congestion, energy consumption, and excessive pollution, big data gathered from legacy systems (e.g., sensors not conformant with modern standards), geographic information system...

Nowadays cities, due to the increasing urbanization, are facing challenges spanning on multiple domains as mobility, energy, environment, etc. Big data gathered from legacy systems, from geographic information systems, operators, and Internet of Things technologies can be exploited to provide insights to assess the current status of a city, the pos...

The number of data sources and models in the mobility and transport domain strongly proliferated in the last decade. Most formats have been created to enable specific and innovative applications. On the other hand, the available data models present a certain degree of complexity in terms of their integration and management due to partial overlaps,...

Dyck paths having height at most $h$ and without valleys at height $h-1$ are combinatorially interpreted by means of 312-avoding permutations with some restrictions on their \emph{left-to-right maxima}. The results are obtained by analyzing a restriction of a well-known bijection between the sets of Dyck paths and 312-avoding permutations. We also...

Looking for available parking slots has become a serious issue in urban mobility, since it influences traffic and emissions. This paper presents a set of metrics and techniques to predict the number of available parking slots in off-street parking facilities. This study deals with deep learning model solutions according with a mid-term prediction o...

Traffic management and sustainable mobility are the central topics for intelligent transportation systems (ITS). By means of modern technologies, it is possible to collect real-time traffic flow data to extract useful information to monitor and control vehicular traffic. On the other hand, costs to obtain this piece of information are high. It requ...

A main key success for public transportation networks is their tuning by the analysis of mobility demand with respect to the offer in terms of public transportation means. Most of the solutions at the state of the art have strong limitations in taking into account: multiple contextual information as attractors/motivations for people movements, moda...

CO2 emissions from burning fossil fuels make a relevant contribution to atmospheric changes and climate disruptions. In cities, the contribution by traffic of CO2 is very relevant, and the general CO2 estimation can be computed (i) on the basis of the fuel transformation in energy using several factors and efficiency aspects of engines and (ii) by...

Nowadays, traffic management and sustainable mobility are central topics for intelligent transportation systems (ITS). Thanks to new technologies, it is possible to collect real-time data to monitor the traffic situation and contextual information by sensors. An important challenge in ITS is the ability to predict road traffic flow data. The short-...

Drastic changes into city road traffic may impact in large portions of the city, then hypothetical scenarios have to be analyzed to identify the best solutions to maintain high quality of city services. In this paper, a solution for unexpected or planned events is proposed and validated with the major focus on traffic flow fields. In order to mitig...

Forecasting future values of air quality related metrics and specific pollutant concentration could be of pivotal importance in recent Smart City perspectives. A number of pollutants are dangerous for people’s health and impact on environment and climate. In order to control and reduce the emissions, national and international organizations have de...

According to the COVID-19 lockdown and successive reopening a number of facts can be analysed. The main effects have been detected on: mobility and environment, and specifically on traffic, environmental data and parking. The mobility reduction has been assessed to be quite coherent with respect to what has been described by Google Global mobility...

In recent years, there is an increasing attention on air quality derived services for the final users. A dense grid of measures is needed to implement services such as conditional routing, alerting on data values for personal usage, data heatmaps for Dashboards in control room for the operators, and for web and mobile applications for the city user...

The knowledge of the real time traffic flow status in each segment of a whole road network in a city or area is becoming fundamental for a large number of smart services such as: routing, planning, dynamic tuning services, healthy walk, etc. Rescue teams, police department, and ambulances need to know with high precision the status of the network i...

According to the changed operative conditions due to lockdown and successive reopening a number of facts can be analysed. The main effects have been detected on: mobility, environment, social media and people flows. While in this first report only mobility, transport and environment are reported. The analysis performed identified a strong reduction...

We define a set of binary matrices where any two of them can not be placed one on the other in a way such that the corresponding entries coincide. The rows of the matrices are obtained by means of Dyck words. The cardinality of the set of such matrices involves Catalan numbers.

We define a set of matrices over a finite alphabet where all possible overlaps between any two matrices are forbidden. The set is also enumerated by providing some recurrences counting particular classes of restricted words. Moreover, we analyze the asymptotic cardinality of the set according to the parameters related to the construction of the mat...

In this paper we give a combinatorial interpretation of linear recurrences having constant coefficients. In particular, we describe a recursive construction for a language L such that the words in L having length n satisfy the given recurrence and avoid a cross-bifix-free set of patterns.

In this paper we present a method to pass from a given recurrence relation with constant coefficients (in short, a C-finite recurrence) to a finite succession rule defining the same number sequence. Our method consists in two steps: first, we transform the given recurrence relation into an extended succession rule, then we provide a series of opera...

We define a variable-length code having the property that no (non-empty) prefix of each its codeword is a suffix of any other one, and vice versa. This kind of code can be seen as an extension of two well-known codes in literature, called respectively fix-free code and non-overlapping code. In this paper, some constructive algorithms for such codes...

We define a variable-length code having the property that no (non-empty) prefix of each its codeword is a suffix of any other one, and vice versa. This kind of code can be seen as an extension of two well-known codes in literature, called respectively fix-free code and non-overlapping code. In this paper, some constructive algorithms for such codes...

Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the $k$-generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily s...

Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the $k$-generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily s...

Minimal permutations with d descents and size d+2 have a unique ascent between two sequences of descents. Our aim is the enumeration of two particular sets of these permutations. The first set contains the permutations having d+2 as the top element of the ascent. The permutations in the latter set have 1 as the last element of the first sequence of...

We study the construction and the enumeration of bit strings, or binary words in {0, 1}*, having more 1’s than 0’s and avoiding a set of Grand Dyck patterns which form a cross-bifix-free set. We give a particular jumping and marked succession rule which describes the growth of such words according to the number of 1’s. Then, we give the enumeration...

In this paper we present a method which can be used to investigate on the positivity of a number sequence defined by a recurrence relation having constant coefficients (in short, a \(C\)-recurrence).

A bidimensional bifix (in short bibifix) of a square matrix T is a square submatrix of T which occurs in the top-left and bottom-right corners of T. This allows us to extend the definition of bifix-free words and cross-bifix-free set of words to bidimensional structures. In this paper we exhaustively generate all the bibifix-free square matrices an...

A set of words with the property that no prefix of any word is the suffix of any other word is called cross-bifix-free set. We provide an efficient generating algorithm producing Gray codes for a remarkable family of cross-bifix-free sets.

Cross-bifix-free sets are sets of words such that no prefix of any word is a sufix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free q-ary words of fixed length. It enables us to determine a cross-bifix-free words subset which has the property to be non-expandable.

We study a problem involving the reconstruction of an image from its horizontal and vertical projections in the case where some parts of these projections are unavailable. The desired goal is to model applications where part of the x-rays used for the analysis of an object are blocked by particularly dense components that do not allow the rays to p...

Based on BRGC inspired order relations we give Gray codes and a generating algorithm for $q$-ary words avoiding a prescribed factor. These generalize an early 2001 result and a very recent one published by some of the present authors, and can be seen as an alternative to those of Squire published in 1996. Among the involved tools, we make use of ge...

A cross-bifix-free set of words is a set in which no prefix of any length of any word is the suffix of any other word in the set. A construction of cross-bifix-free sets has recently been proposed by Chee {\it et al.} in 2013 within a constant factor of optimality. We propose a \emph{trace partitioned} Gray code for these cross-bifix-free sets and...

We provide a trace partitioned Gray code for the set of q-ary strings avoiding a pattern constituted by k consecutive equal symbols. The definition of this Gray code is based on two different constructions, according to the parity of q. This result generalizes, and is based on, a Gray code for binary strings avoiding k consecutive 0's.

In this paper we consider the class of column-convex permutominoes, i.e. column-convex polyominoes defined by a pair of permutations π1, π2. First, using a geometric construction, we prove that for every permutation π there is at least one column-convex permutomino P such that π1P = π or π2P = π. In the second part of the paper, we show how, for an...

Let F[p] denote the set of binary words, with no more 0's than 1's, that do not contain the pattern p = (10)j1 as a factor for any fixed j ≥ 1. We give the generating function for the integer sequence enumerating, according to the number of 1's, the words in F[p].

In this paper we study the construction and the enumeration of binary words in $\{0,1\}^*$ having more 1’s than 0’s and avoiding a set of cross-bifix-free patterns. We give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of a...

In this paper we present a method to pass from a recurrence relation having constant coefficients (in short, a C-recurrence) to a finite succession rule defining the same number sequence. We recall that succession rules are a recently studied tool for the enumeration of combinatorial objects related to the ECO method. We also discuss the applicabil...

In this paper we propose an algorithm to generate binary words with no more 0's than 1's having a fixed number of 1's and avoiding the pattern $(10)^j1$ for any fixed $j \geq 1$. We will prove that this generation is exhaustive, that is, all such binary words are generated.

In this paper we study the enumeration and the construction of particular binary words avoiding the pattern 1j+10j. By means of the theory of Riordan arrays, we solve the enumeration problem and we give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones...

Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to determine a cross-bifix-free words subset which has the property to be non-expandable.

In this paper we study the enumeration and the construction, according to the number of ones, of particular binary words avoiding a fixed pattern. The growth of such words can be described by particular jumping and marked succession rules. This approach enables us to obtain an algorithm which constructs all binary words having a fixed number of one...

In this paper we study the enumeration and the construction of particular binary words avoiding the pattern $1^{j+1}0^j$. By means of the theory of Riordan arrays, we solve the enumeration problem and we give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number o...

A Catalan pair is a pair of binary relations (S,R) satisfying certain axioms. These objects are enumerated by the well-known Catalan numbers, and have been introduced with the aim of giving a common language to most of the structures counted by Catalan numbers. Here, we give a simple method to pass from the recursive definition of a generic Catalan...