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The focus of the course is to give an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the power of techniques in algebraic combinatorics. Rigorous mathematical proofs, rational generating functions and Recurrence relations and Adjacency and Laplacian matrices of graphs are expected in this course.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: MIT

Course Curriculum

Introduction to course, walks on graphs, rational generating functions and Fibonacci numbers 00:10:00
Partially ordered sets II Dilworth’s and Sperner’s theorem 00:10:00
Partially ordered sets III the Mobius function 00:10:00
Introduction to partitions and two proofs of Euler’s theorem 00:15:00
Partitions II Euler Pentagonal theorem and other identities 00:10:00
Proof of Schensted’s theorem 00:10:00
An introduction to symmetric functions 00:15:00
Symmetric functions II 00:15:00
Polya theory III, intro to exponential generating functions 00:10:00
Exponential generating functions and tree enumeration 00:10:00
Tree enumeration II 00:10:00
Eulerian tours II 00:10:00
Chip firing games I 00:20:00
Chip firing games II the critical group 00:20:00
Chip firing games III proof of uniqueness 00:20:00
Perfect matchings and Domino tilings 00:10:00
Lattice path enumeration II 00:20:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

Course Reviews

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