Combinatorics and Number Theory of Counting Sequences (Paperback)

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.

《排列組合與數論的計數序列》是一本介紹有限集合分割理論和排列的循環分解計數的入門書籍。

該書的呈現方式優先考慮基礎的計數證明。因此，書中的部分內容設計得即使是對組合學感興趣的高中生和教師也能受益。同時，該書收集了許多計數序列的最新資訊（尤其是與集合分割和排列有關），因此對於從事組合計數研究的數學家來說，這是一本必備的參考書。

此外，該書還包含了關於集合分割和排列計數序列的數論結果，因此對於希望在組合學中看到他們感興趣領域的應用的數論學家來說，這本書也很有價值。

特點：
- 每章結束時的展望部分引導讀者探索書中未涉及的主題，其中許多展望項目指向新的研究問題。
- 書末的廣泛參考文獻和表格使該書成為一本標準參考書。
- 引用散落在文獻中的結果現在變得容易，因為該書的大部分內容（尤其是第二部分和第三部分）首次以書籍形式出現。

István Mező is a Hungarian mathematician. He obtained his PhD in 2010 at the University of Debrecen. He was working in this institute until 2014. After two years of Prometeo Professorship at the Escuela Politécnica Nacional (Quito, Ecuador) between 2012 and 2014 he moved to Nanjing, China, where he is now a full-time research professor.

István Mező is a Hungarian mathematician. He obtained his PhD in 2010 at the University of Debrecen. He was working in this institute until 2014. After two years of Prometeo Professorship at the Escuela Politécnica Nacional (Quito, Ecuador) between 2012 and 2014, he moved to Nanjing, China, where he is now a full-time research professor.