This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more…
The life and soul of any science are its problems. This is particularly true of mathematics, which, not referring to any physical reality, consists only of its problems, their solutions, and, most excitingly, the challenges they pose. Mathematical problems come in many flavours,…
This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov's pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at a…
The study of discrete mathematics is one of the first courses on curricula in various educational disciplines such as Computer Science, Mathematics and Engineering. Graphs are key data structures used to represent networks, chemical structures, games etc. and are increasingly us…
This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-de…
Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computati…
This book uses literature as a wrench to pry open social networks and to ask different questions than have been asked about social networks previously. The book emphasizes the story-telling aspect of social networks, as well as the connection between narrative and social network…
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer's Problem (1933) and …
This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, allianc…
Marking 94 years since its first appearance, this book provides an annotated translation of Sainte-Laguë's seminal monograph Les réseaux (ou graphes), drawing attention to its fundamental principles and ideas. Sainte-Laguë's 1926 monograph appeared only in French, but in the 199…
The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several othe…
The 9th issue of the Transactions on Computational Science journal, edited by François Anton, is devoted to the subject of Voronoi diagrams in science and engineering. The 9 papers included in the issue constitute extended versions of selected papers from the International Sympo…
A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, an…
