MA 319: Algebraic Combinatorics

Instructors: Arvind Ayyer and Digjoy Paul
Office: X-15 and N-22
Phone number: (2293) 3215 for AA
Email: (First name and First+Last name) at math dot iisc dot ernet dot in
Class Timings: Tuesday and Thursday -- 2:00–3:30pm.
Classroom: LH 3, Mathematics Department (ground floor)
Office hours: By appointment
Textbook: Enumerative Combinatorics: Volume 2
by Richard P. Stanley, Cambridge University Press
ISBN-13 - 978-0521560696

Representation Theory : A Combinational Viewpoint
by Amritanshu Prasad, Cambridge studies in applied mathematics
ISBN-13 - 978-1107082052

The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions
by Bruce Sagan, Springer
ISBN-13 - 978-1441928696

Course Prerequisites

No prior knowledge of combinatorics is expected, but a familiarity with linear algebra and finite groups will be assumed.

Course Description

The algebra of symmetric functions, Schur functions, RSK algorithm, Murnaghan-Nakayama Rule,
Knuth equivalence, jeu de taquin, evacuation, Littlewood-Richardson rules,
Advanced topics.

Computer Programming

We will spend a couple of lectures learning symbolic programming.
Possible software choices are Maple, Mathematica and the free and open source python-based Sage.

Exams

All exams will be closed book, closed notes, and
no calculators or electronic devices are allowed.
No communication among the students will be tolerated.
There will be no make up exams.

The date for the final exam will be announced later.


Grading

Here are the weights for the homework and exams.
All marks will be posted online on Moodle.


Tentative Class Plan

Week 1 (Jan 4): Introduction to Symmetric functions

Week 2 (Jan 11): Various bases and structure constants

Week 3 (Jan 18): Young tableaux and Schur functions

Week 4 (Jan 25): Schensted's algorithm and RSK correspondence

Week 5 (Feb 1): Variants of RSK correspondence and applications

Week 6 (Feb 8): Pieri's rule and Jacobi-Trudi identity

Week 7 (Feb 15): Murnaghan-Nakayama rule

Week 8 (Feb 22): Midterm week, no classes
Midterm on Feb 22

Week 9 (Feb 29): Knuth equivalence, Jeu de Taquin, Schutzenberger involution

Week 10 (Mar 7): Littlewood-Richardson rule

Week 11 (Mar 14): TBD

Week 12 (Mar 21): TBD

Week 13 (Mar 28):TBD

Week 14 (Apr 4):TBD

Week 15 (Apr 11): TBD

Week 16 (Apr 18): TBD

Final TBD