Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research. Each chapter presents new methods and techniques by leading experts. Unifying interdisciplinary applications, problems, and approaches of discrete mathematics, this book connects topics in graph theory, combinatorics, number theory, cryptography, dynamical systems, finance, optimization, and game theory. Graduate students and researchers in optimization, mathematics, computer science, economics, and physics will find the wide range of interdisciplinary topics, methods, and applications covered in this book engaging and useful.

Autorentext
**Andrei Raigorodskii is a Federal Professor of Mathematics at the Moscow Institute of Physics and Technology (MIPT) where he is the Director of the Phystech-School of Applied Mathematics and Computer Science, the Head of the Discrete Mathematics Department, the Head of the Laboratory of Advanced Combinatorics and Network Applications, as well as the Head of the Laboratory of Applied Research MIPT-Sberbank. He is also the Head of the Caucasus Mathematical Center. He lectures at MIPT, MSU, HSE and has published about 200 papers and 20 books. He is the Editor-in-Chief of the Moscow Journal of Combinatorics and Number Theory. In 2011, he was awarded the 2011 Russian President's Prize in Science and Innovation for young scientists.
Michael Th. Rassias** is currently a Latsis Foundation Senior Fellow at the University of Zürich, a visiting researcher at the Institute for Advanced Study, Princeton, as well as a visiting Assistant Professor at the Moscow Institute of Physics and Technology. He obtained his PhD in Mathematics from ETH-Zürich in 2014. During the academic year 2014-2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F. Nash, Jr. the volume "Open Problems in Mathematics", Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. He has authored and edited several books with Springer. His current research interests lie in mathematical analysis, analytic number theory, zeta functions, the Riemann Hypothesis, approximation theory, functional equations and analytic inequalities.

Inhalt
Automatic sequences are also non-uniformly morphic (Allouche).- Combinatorial Identities and Inequalities for Trigonometric Sums (Alzer).- The number of partitions of a set and superelliptic Diophantine equations (Andrica).- The exponent of a group: properties, computations and applications (Andrica).- Hankel Tournaments and Special Oriented Graphs (Brualdi).- The game chromatic number of a random hypergraph (Chakraborti).- Perfect Hash Families: The Generalization to Higher Indices (Dougherty).- A note on randomly colored matchings in random bipartite graphs (Funkhouser).- Exponential variational integrators using constant or adaptive time step (Kostochka).- A new embedding of the 3x + 1 dynamical system (Leventides).- Diffusion on dynamical interbank loan networks (Leventides).- The dynamics of interbank networks (Leventides).- Prime avoidance property of k-th powers of prime numbers with Beatty sequences (Maier).- A survey of hypergraph Ramsey problems (Mubayi).- Factorization Method for Solving Multipoint Problems for Second Order Difference Equations with Polynomial Coefficients (Parasidis).- New Construction Machines of Generating Fuzzy Implications (Rapti).- Tree containment and degree conditions (Stein).- Extremal singular graphs (Triantafillou).