Combinatorics and Number Theory of Counting Sequences

<p><strong><em>Combinatorics and Number Theory of Counting Sequences</em></strong> is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations.</p><p></p><p>The presentation prioritizes elementary enumerative proofs. Therefore parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still the book collects vast up-to-date information for many counting sequences (especially related to set partitions and permutations) so it is a must-have piece for those mathematicians who do research on enumerative combinatorics.</p><p></p><p>In addition the book contains number theoretical results on counting sequences of set partitions and permutations so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book too.</p><p>Features</p><p></p><ul> <p/><p></p> <li>The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book and many of the Outlook items point towards new research problems.</li> <p/> <p/><p></p> <li>An extensive bibliography and tables at the end make the book usable as a standard reference.</li> <p/> <p/><p></p> <li>Citations to results which were scattered in the literature now become easy because huge parts of the book (especially in parts II and III) appear in book form for the first time.</li> <p/> </ul><p></p>