Combinatorics and Number Theory of Counting Sequences

Combinatorics and Number Theory of Counting Sequences

Mezo, Istvan

Taylor & Francis Ltd

01/2023

498

Mole

Inglês

9781032475356

15 a 20 dias

920

Descrição não disponível.
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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Bell Polynomials;Stirling Numbers;Negative Real Line;Exponential Generating Function;Meixner Polynomials;Universal Generating Functions;Bell Number;Minimal Polynomial;Log Concave Sequence;Hankel Transform;Eulerian Polynomial;Hankel Determinant;Pascal Triangle;Power Sum;Eulerian Numbers;Cauchy Number;Combinatorial Proof;Riemann Zeta Function;Binomial Coefficients;Bernoulli Polynomials;Young Tableau;Characteristic Polynomial;Bernoulli Numbers;Bessel Polynomials;Euler Gamma Function