Algebraic Combinatorics

By Prof. Amritanshu Prasad, Prof. S. Viswanath | The Institute of Mathematical Sciences, Chennai

Learners enrolled: 685

About the Course:

The objective of this course is to introduce the student to some powerful paradigms in modern combinatorics, namely Möbius inversion on partially ordered sets, combinatorial classes and combinatorial species, and the Lindström-Gessel-Viennot lemma. It will also include an introduction to the theory of symmetric functions.

INTENDED AUDIENCE: M.Sc./M.Tech. (Mathematics, Computer Science), PhD coursework (Mathematics, Computer Science), advanced undergraduates, B.Sc., B.E., B.Tech. (Mathematics, Computer Science).
PREREQUISITES: Knowledge of set theory, linear algebra, and algebra at the undergraduate level, basic undergraduate discrete mathematics (induction, graphs, trees, basic counting techniques, recurrence relations, etc.).
INDUSTRY SUPPORT: Nil

Summary

Course Status :	Completed
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Algebra Mathematics
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	24 Jan 2022
End Date :	15 Apr 2022
Enrollment Ends :	07 Feb 2022
Exam Date :	24 Apr 2022 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Partially ordered sets and Möbius inversion

Week 2: Finite distributive lattices
Week 3: Combinatorial classes and their ordinary generating functions
Week 4: Operations on combinatorial classes
Week 5: Combinatorial specifications
Week 6: Groups of permutations, cycle structure, orbit counting method
Week 7: Polya’s enumeration theorem, the cycle index generating function
Week 8: Combinatorial species and associated generating functions
Week 9: Operations on species
Week 10: The LGV lemma
Week 11: Symmetric functions – elementery, complete, power sum
Week 12: Symmetric functions – Schur functions

Books and references

1.Enumerative Combinatorics (2 vols) by Richard Stanley

2.Analytic Combinatorics by Flajolet and Sedgewick

3.Combinatorial Species and tree-like structures by Bergeron, Labelle and Leroux

4.An introduction to Schur polynomials by Amritanshu Prasad (https://arxiv.org/abs/1802.06073)

5.Algebraic Combinatorics: Walks, Trees, Tableaux, and More, by Richard Stanley

Instructor bio

Prof. Amritanshu Prasad

Amritanshu Prasad is a faculty at The Institute of Mathematical Sciences, Chennai. His research interest is in representation theory.

Prof. S. Viswanath

The Institute of Mathematical Sciences, Chennai

S Viswanath is a faculty at The Institute of Mathematical Sciences, Chennai. His research interest is in representation theory.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: 24 April 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup. It will have the logos of NPTEL and IIT Madras. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team