About the book
Combinatorial mathematics primarily deals with combining and arranging countable collections of finite sets or structures. The fundamental principles of counting, such as permutations and combinations, are deeply rooted in ancient Chinese, Hindu, Arab and Jewish cultures. In the last two decades, the subject has grown up rapidly reaching the level of a mature field of mathematics, but also thanks to the recognition of outstanding mathematicians who have been awarded Fields Medals for making extensive use of methods from combinatorial theory (e.g. Timothy Gowers in 1998 and Terence Tao in 2006).
Combinatorics has links with several other mathematics area, for example, with graph theory, linear algebra, probability, discrete optimisation, coding theory, designs theory, finite geometry, topology, cryptography, to name only a few. This development has been vigorously accelerated by the advent of digital computers, and is greatly benefiting from synergies with the emerging areas of machine and deep learning, artificial intelligence, intelligent systems.
The book collects research papers from world leading experts in combinatorial mathematics, highlighting ongoing trends, progress and open problems in this fascinating and critically important area of modern science. Since theory is often motivated primarily by examples, considerable attention will be given to applied problems.