Eulerian Numbers

The main purpose of the book is to give a complete presentation of the Theory of a well-known class of special numbers (Eulerian numbers), as well as some generalizations and relatives (Eulerian numbers of the second order, factorial numbers, Euler numbers, etc.), and to give much of their properties, facts and theorems with full proofs.The 'names' of many of the special numbers essential to so many aspects of Number Theory, general Mathematics, and several applied areas are known to every mathematician. Fermat numbers, Mersenne numbers, Fibonacci numbers, etc. Yet actual information on them is often scattered in the actual literature, and those books which do provide this information are often by now out of date. This series is committed to remedying this gap, and this title in particular is dedicated to Eulerian numbers, their relatives, and their generalizations.Key definitions, collected main properties of considered mathematical objects, the integral main facts of the theory of set-partitions, recurrent equations, and generating functions, the main questions of Eulerian numbers of the first- and second-orders, comprehensive and exclusive collections of practice exercises, a huge Mini Dictionary, and much more is compiled and presented in this text to provide an accessible guide to the field for not only undergraduate students of Mathematics but also for professionals and the general interested audience.