MA 318: Combinatorics
Instructor:

Arvind Ayyer

Office:

X15 (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
ISBN13  9781568812793
Freely downloadable from
here
Enumerative Combinatorics: Volume 1 (Second Edition)
by Richard P. Stanley
ISBN13  9781107602625
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 inclusionexclusion, 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.
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 midterm and final 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% – Quizzes and Homeworks
 30% – Midterm (February 21, LH1, 2  4pm)
 50% – Final (April 22, LH1, 9am  12pm)
Tentative Class Plan
Week 1: Introduction and programming
Chapter 1 of Wilf
Weeks 23: Formal power series
Chapter 2 of Wilf
Week 4: Sets and Permutations
1.21.3 of Stanley
Week 56: Permutation Statistics
1.31.6 of Stanley
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
Week 9: Partitions
1.8 of Stanley
Week 10: The exponential and "Ordinary" formulae
Chapter 3 of Wilf
Week 11: Counting with symmetry & Combinatorial Identities
4.34.4 of Wilf
Week 12: Posets and Lattices
3.13.7 of Stanley
Week 13: Finals week
Final exam on Apr 22, LH1, 9am  12pm