MA 319: Algebraic Combinatorics
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Instructors:
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Arvind Ayyer and Digjoy Paul
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Office:
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X-15 and N-22
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Phone number:
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(2293) 3215 for AA
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Email:
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(First name and First+Last name) at math dot iisc dot ernet dot in
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Class Timings:
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Tuesday and Thursday -- 2:00–3:30pm.
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Classroom:
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LH 3, Mathematics Department (ground floor)
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Office hours:
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By appointment
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Textbook:
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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
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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 on Sage using CoCalc.
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.
- 5% – Attendance
- 15% – Homeworks
- 30% – Midterm
- 50% – Final
Tentative Class Plan
Week 1 (Jan 1): Introduction to Symmetric functions
Week 2 (Jan 8): Various bases and structure constants
Homework 1 is here and is due on Jan 30
Week 3 (Jan 15): Young tableaux and Schur functions
Week 4 (Jan 22): Schensted's algorithms and Pieri's rules
Week 5 (Jan 29): RSK correspondence and applications
Week 6 (Feb 5): Viennot's geometric RSK correspondence
Homework 2 is here and is due on Feb 27
Week 7 (Feb 12): LGV lemma, Jacobi-Trudi and Giambelli's identity
Week 8 (Feb 19): Midterm week, no classes
Midterm on Feb 22
Week 9 (Feb 26): Murnaghan-Nakayama rule
Week 10 (Mar 4): Representation theory of symmetric and general linear groups
Week 11 (Mar 11): Knuth equivalence, Jeu de Taquin
Week 12 (Mar 18): Evacuation, and promotion for posets
Week 13 (Mar 25): Littlewood-Richardson rule
Week 14 (Apr 1): TBD
Week 15 (Apr 8): TBD
Final TBD