Combinatorics and number theory of counting sequences
著者
書誌事項
Combinatorics and number theory of counting sequences
（Discrete mathematics and its applications / Kenneth H. Rosen, series editor）
CRC Press, c2020
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注記
Includes bibliographical references (p. 433-471) and index
"A Chapman & Hall book"--Cover
内容説明・目次
内容説明
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.
目次
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
「Nielsen BookData」 より
