ISL Combinatorics (2012)

In this school, we mainly plan to cover Introduction to Combinatorics by Martin J. Erickson. More precisely, we plan to cover the following topics: Review of Set Theory, Algebra and Number Theory, The Pigeonhole Principle (many versions), Extremal graphs, Coloring of the plane, Sequences and Partial orders (including Erdos -Szekeres Theorem, Dilworth’s Lemma, Sperner’s Theorem), Ramsey Theory (including Vander Waerden’s Theorem), The fundamental Counting Problem,Recurrence Relations and Explicit Formulas, Permutations andTableaux, The Polya Theory of counting, Codes and Designs.

Syllabus

 We will be covering  the book "Introduction to Combinatorics'' by M. J. Erickson.

• Chapters 1 and 2:  Preliminaries and The pigeonhole principle: Dr. B. K. Sharma will be covering in 5 lectures and 3 tutorials.
• Chapters 3 and 4: Sequences and Partial orders and Ramsey Theory: Professor S. D. Adhikari  will be covering in 5 lectures and 3 tutorials.
• Chapters 5 and 6:  Fundemental Counting Problem and recurrence relations: Dr. R. Thangadurai  will be covering in 5 lectures and 3 tutorials.
• Chapter 7 and 8: Permutations and Tableaux and Polya Theory of Counting: Professor A. Prasad will be covering in 5 lectures and 2 tutorials.
• Chapter 9 and 10: Codes and Designs: Professor S. Sane will be covering in 5 lectures  and 2 tutorials

Apart from these, there will be five general lectures 

• Professor S. D. Satya Deo will be giving two general lectures on Borsuk Ulam Theorem.
• Dr. D. S. Ramana will be delivering two general lectures on Counting problems.
• Professor B. Ramakrishnan will be giving a lecture on Partition function.
• 3 hours we have kept for Seminar by Participants.

Time Table

(1) Main Lectures are of one and a half hours duration.
(2) One hour talks are either tutorials or general lectures.

• The selected candidates will be receiving their selection letter through email.
• Those who have not got email by 16th March, 2012. Kindly write to kr.thangadurai at gmail.com.
• Those who have got the selection letter must confirm their participation by 19th March, 2012 by sending email.
• If we don't receive confirmation mail by 19th March, the selection will be canceled and the position will be given to the candidates who are in the waiting list.

In Allahabad, Harish-Chandra Research Institute is known as HRI. The Institute campus is 13 Kms away from Allahabad junction railway Station. Allahabad  junction  railway station has two sides namely `City side' and `Civil Lines side'.
 
(1) If you come out of the `civil lines side', you need to catch Cycle/Auto rickshaws to reach
our city guest house. Our Institute buses run between the campus and the Institute city guest
house (for technical reasons, it is called HRI camp office) at a regular interval.  The city
guest house is located at:
 
                    HRI City Guest House
                    10A, Kutchery Road (K.G. Marg)
                    Allahabad 211 002,India
                    Phone: +91 (532) 2548 140, 2548 150

 
The city guest house is about 5 Kms from the civil lines side of Allahabad Junction Railway Stataion. You can get cycle rickshaws for about Rs. 15 or 20/- or auto rickshaws (rare to see)for about Rs. 50/- to reach our city guest house. While taking cycle/auto rickshaws, you should tell him that you want to go to Police Lines near State Bank of India (Main branch). Once you see the State bank of India on your right hand side, in just few meters, you will see HRI City Guest House on your right side. Opposite to State bank of India is the Police lines. In the city guest house), round the clock, at least one  security guard is posted and one can check with him the bus timings of HRI
to come to the HRI campus.

(2) If  you come out of `city side' of the Railway Station (which is the main side), then to reach HRI city guest house, one need to take tempo (3 wheelers). To catch tempos, first you have to come out of the railway station. Ask the tempo drivers whether it will go to Civil lines Hanuman Mandir. Wherever you get down at Civilines Hanuman Mandir, you can catch another tempo to go to Police Lines or State bank of India. Once you reach State bank of India, you follow the same path described in (1). 

(3) If you come as a group, then you can hire a whole tempo (3 wheelers) to come directly to theHRI campus (rate is about Rs. 250/-). One may have to bargain a bit. This tempos are available inthe city side (not the civil lines side) of the Allahabad Junction Railway Station. You should tell him that you want to go to Chhatnag Ghat, Jhunsi. Possibly he will be knowing HRI. If not,you can tell him that you have to go to Birla school. Just before Birla school, HRI campus is situated. The enroute to the campus from Allahabadn Railway station is the following. It will take you through densely populous road upto `toll gate' which is just before 'Sastri Bridge' over the holi river Ganges. Then it will continue its journey in the G. T. Road (Grand Trunk road).About 4kms journey from Sastri Bridge, it has to take a right turn (turning point is known as`Chuk')  at which there is a sign board of HRI as well as Birla school or Bank of Baroda at HRI campus.  From this point, another 3 Kms to reach the campus through the village road. This road leads to the river Ganges (the Ghat is called Chhatnag Ghat and hence this road is called Chhatnag Road). After HRI campus, Birla school and Sada Phal Ashram are there. People know about
either Biral School or Sada Phal Ashram.