CiNii 図書 - Combinatorics and number theory of counting sequences

Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. 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. 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. Features 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. An extensive bibliography and tables at the end make the book usable as a standard reference. 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.

I Counting sequences related to set partitions and permutations Set partitions and permutation cycles. Generating functions The Bell polynomials Unimodality, log concavity and log convexity The Bernoulli and Cauchy numbers Ordered partitions Asymptotics and inequalities II Generalizations of our counting sequences Prohibiting elements from being together Avoidance of big substructures Prohibiting elements from being together Avoidance of big substructures Avoidance of small substructures III Number theoretical properties Congurences Congruences vial finite field methods Diophantic results Appendix

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Combinatorics and number theory of counting sequences

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