Combinatorialists are seldom aware of number theoretical tools, and number theorists rarely aware of possible combinatorial applications. This book is accessible for both of the groups. The first part introduces important counting sequences. The second part shows how these sequences can be generalized to study new combinatorial problems
Combinatorialists are seldom aware of number theoretical tools, and number theorists rarely aware of possible combinatorial applications. This book is accessible for both of the groups. The first part introduces important counting sequences. The second part shows how these sequences can be generalized to study new combinatorial problems
István Mez¿ 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.
Inhaltsangabe
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
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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