1st Edition

Combinatorics and Number Theory of Counting Sequences

By Istvan Mezo Copyright 2020
    498 Pages 10 B/W Illustrations
    by CRC Press

    498 Pages 10 B/W Illustrations
    by Chapman & Hall

    498 Pages 10 B/W Illustrations
    by Chapman & Hall

    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



     

    Biography

    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.