INSTITUTE OF APPLIED MATHEMATICS
Last Updated:
21/07/2017 - 12:25

IAM506 - Combinatorics

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Consent of IAM
Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Algebraic Enumeration Methods: Bijections, generating functions, free monoids. Lagrange inversion, multisets and partitions. Inclusion-Exclusion, Mobius inversion, symmetric functions. Asymptotic Enumeration: Estimation of sums, formal power series, elementary estimates for convergent generating functions, analytical generating functions, singularities, Darboux’s theorem, algorithmic and automated asymptotics. External set systems: Intersecting families, families with prescribed intersection sizes, s-wise t-intersection families, covering number. Computational complexity.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Algebraic Enumeration Methods: Bijections, generating functions, free monoids. Lagrange inversion, multisets and partitions. Inclusion-Exclusion, Mobius inversion, symmetric functions. Asymptotic Enumeration: Estimation of sums, formal power series, elementary estimates for convergent generating functions, analytical generating functions, singularities, Darboux’s theorem, algorithmic and automated asymptotics. External set systems: Intersecting families, families with prescribed intersection sizes, s-wise t-intersection families, covering number. Computational complexity.

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