Homework 1
Combinatorics I (Fall 2012)
Rutgers University
Swastik Kopparty
Due Date: September 24, 2012.
1. Let (an ) be a sequence of complex numbers. Show that an is a linear-recurrent sequence
n=0
if and only if there exist 1 , . . . , k C and polynomi
Homework 2
Combinatorics I (Fall 2012)
Rutgers University
Swastik Kopparty
Due Date: October 22, 2012.
1. Let be a nite set, with | = q . For a sequence s, let |s| denote its length.
Let s1 , s2 , . . . , sk be (nonempty) sequences composed of elements fr
Homework 3
Combinatorics I (Fall 2012)
Rutgers University
Swastik Kopparty
Due Date: November 19, 2012.
1. Generalize the Erdos-Rado argument from class to show the following relationship between
2-color k -uniform hypergraph Ramsey numbers and 2-color k
Homework 4
Combinatorics I (Fall 2012)
Rutgers University
Swastik Kopparty
Due Date: December 5, 2012.
1. Let be a nite set of cardinality q . Formulate and prove a version of the Sauer-Shelah
lemma for subsets of n (The original Sauer-Shelah lemma deals