Combinatorics 1
August- November 2016

Click here for the homeworks.
Lectures: Mondays and Thursdays from 4:45 to 6:00 pm
Classroom: Lecture Hall 4
Instructor: Priyavrat Deshpande.
Contact: Office: 403
phone: 962
email: pdeshpande AT cmi DOT ac DOT in
Office Hours:
 Mondays and Thursdays from 3:30 to 4:30 in 405
Texts:
  • Enumerative Combinatorics (volume 1) by Richard Stanley.
Useful reading material:
  • Introduction to geometric probability by Klain and Rota
  • Arrangements of hyperplanes by Orlik and Terao
  • Hyperplane Arrangements by Richard Stanley. Web link
Prerequisites:     Algebra 2, Topology  and/or permission from the faculty advisor.
Grading:
  • Homework 40%
  • Mid semester exam 30%
  • End semester exam 30%
Web: http://www.cmi.ac.in/~pdeshpande/com16.html
Course syllabus

This course will focus on order theoretic structures, Mobius inversion, incidence algebras, Euler characteristic as a valuation and hyperplane arrangements. Towards the end I will concentrate on Coxeter arrangements that arising due to actions of finite reflection groups. This course should serve as a prerequisite for Combinatorics 2 being offered the following semester by Vijay Ravikumar. The aim of Combinatorics 2 is to understand the combinatorics of Coxeter groups and Schubert calculus.

Homework

The homework will be assigned in class. It is your duty to submit the solutions on time. Copying and/or plagiarism will not be tolerated. Here are a few writing guidelines you might want to follow.
  1. Feel free to work together, but you should submit your own work.
  2. Your questions/comments/suggestions are most welcome. I will also be fairly generous with the hints. However, do not expect any kind of help, including extensions, on the day a homework is due.
  3. Please turn in a neat stapled stack of papers. Refrain from using blank / printing paper. Use ruled paper.
  4. Your final finished version should be as polished as you can make it. This probably means that you cannot submit sketchy solutions or sloppily written first versions. Please expect to do a fair amount of rewriting. Do not hand in work with parts crossed out; either use a pencil and erase or rewrite.
  5. Please write complete sentences that form paragraphs and so forth. It might be a good idea to use short simple sentences; avoid long complicated sentences.
  6. Do use commonly accepted notation (e.g., for functions, sets, etc.) and never invent new notation when there is already some available.
  7. Make sure you provide a statement clearly indicating precisely what it is that you are about to prove. You can, if you want, label your statement as a Theorem or Claim or whatever. Write the word Proof, and then give your proof.
  8. Throughout your writing, constantly tell the reader (i.e. me, :-)) exactly what it is that you are about to demonstrate. Be sure to indicate the end of your proof.
  9. Your answers should combine “logic”, your hypotheses, and possibly other mathematical facts (e.g., theorems that we have proved in class) into an argument that establishes the asserted conclusion.
  10. Please be extra careful about the order in which you use your quantifiers.
  11. In your arguments you can make free use of anything that we have proven in class, and of course all logic rules and basic axioms and definitions. Anything else that you use should be proved.
The Assignments
  1. Homework 1 (pdf) is due on 11/08/2016.
  2. Homework 2 (pdf) is due on 22/08/2016. 
  3. Homework 3 (pdf) is due on 08/09/2016.
  4. Homework 4 (pdf) is due on 10/10/2016.
  5. Homework 5 (pdf) is due on 24/10/2016.
  6. Homework 6 (pdf) is due on 14/11/2016.
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