MA 318: Combinatorics

Instructor: Arvind Ayyer
Office: X-15 (new wing)
Phone number: (2293) 3215
Email: (First name) at math dot iisc dot ernet dot in
Class Timings: Tuesdays and Thursdays, 2:00–3:30pm.
Classroom: LH I, Mathematics Department (first floor)
Office hours: By appointment
Textbook: Generatingfunctionology
by Herbert Wilf
ISBN-13 - 978-1568812793
Freely downloadable from here

Enumerative Combinatorics: Volume 1 (Second Edition)
by Richard P. Stanley
ISBN-13 - 978-1107602625
Older version freely downloadable from here

Course Prerequisites

Calculus, Linear algebra and some exposure to proofs and abstract mathematics.
Programming in Sage will be a part of every lecture. Students will need to bring a laptop with access to the IISc WLAN.

Course Description

Counting problems in sets, multisets, permutations, partitions, trees, tableaux;
ordinary and exponential generating functions;
posets and principle of inclusion-exclusion, the transfer matrix method;
the exponential formula, Polya theory;
bijections, combinatorial identities and the WZ method.

Computer Algebra

We will spend a couple of lectures learning symbolic programming in Sage on the Sage Math Cloud.


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 midterm and final will be announced later.


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

Tentative Class Plan

Week 1: Introduction and programming
Chapter 1 of Wilf
Homework 1
Sage worksheet
Sage worksheet

Weeks 2-3: Formal power series
Chapter 2 of Wilf
Sage worksheet
Sage worksheet

Week 4: Sets and Permutations
1.2-1.3 of Stanley
Sage worksheet
Homework 2

Week 5-6: Permutation Statistics
1.3-1.6 of Stanley
Sage worksheet
Sage worksheet
Sage worksheet
Sage worksheet
Sage worksheet

Week 7: Midterm week
Midterm on Feb 21, LH1, 2 - 4 pm

Week 8: Permutations of Multisets and Twelvefold way
Guest lecture by X. Viennot
Homework 3

Week 9: Partitions
1.8 of Stanley
Sage worksheet
Homework 4

Week 10: The exponential and "Ordinary" formulae
Chapter 3 of Wilf
Sage worksheet
Homework 5

Week 11: Counting with symmetry & Combinatorial Identities
4.3-4.4 of Wilf
Sage worksheet

Week 12: Posets and Lattices
3.1-3.7 of Stanley
Homework 6
Sage worksheet

Week 13: Finals week
Final exam on Apr 22, LH1, 9am - 12pm