Eulerian Numbers

Within these pages readers will find the complete theory of a renowned class of special numbers, Eulerian numbers, as well as some generalisations and relatives (Eulerian numbers of the second order, factorial numbers, Euler numbers, etc.), their properties, their facts, and their theorems, alongside full proofs.

The "names" of many of the special numbers essential to so many aspects of number theory, general mathematics, and numerous applied areas are known to every mathematician: Fermat numbers, Mersenne numbers, Fibonacci numbers, etc. Yet actual information on these numbers is often scattered in the available literature. Those books which do contain such information are often out of date or generalised. It is the goal of this series to remedy this gap.

Among the topics covered in this text are the key definitions, the collected main properties of considered mathematical objects, the main questions of Eulerian numbers of the first- and second-orders, the integral main facts of the theory of set partitions, recurrent equations, and generating functions, and much more. A comprehensive and exclusive collection of practice exercises and an expansive mini dictionary are included to support these points of learning. This comes together to provide an accessible guide to the field of Eulerian numbers for not only undergraduate students of Mathematics but also for professionals and the general interested audience.