MATH 550: Combinatorics. Winter 2013.
Assignment # 3: Discrete Geometry.
Due in class on Wednesday, April 10th.
1.
For X Rd dene S(X) as a set of all points which lie on segments with ends
in X. Let S2 (X) := S(S(X) and, more generally, Sk+1 (X) = S(Sk (X
MATH 550: Combinatorics. Winter 2013.
Assignment #1: Set systems. Due in class on Monday, February 18th.
1.
Bollobs 2.4. Let F [n](2) be such that if Y n, |Y | = n 2, then there exist distinct
a
F1 , F2 F inducing the same subset of Y , that is F1 Y = F2
MATH 550: Combinatorics. Winter 2013.
Assignment # 2: Turn- and Ramsey-type problems.
a
Due in class on Monday, March 11th.
1.
Let (X, F) be a set system. A k-sunower in F is a collection of distinct sets
F1 , F2 , . . . , Fk F such that for some Z X we h
Convex polygons in the plane.
In this note we give two proofs of a Ramsey-type classical theorem of Erdso
Szekeres on convex sets in the plane. We say that a set of points P is in
general position if no three points in P are colinear.
Theorem 1. For every
MATH 550: Combinatorics. Winter 2013.
Final exam.
Due electronically at [email protected]
by 5PM on Tuesday, April 30th.
1.
Turan-type problems.
Consider 3-graphs F4 = cfw_abc, abd, acd and F5 = cfw_abc, abd, cde. We say that a 3-graph
G is cancellati
Erds-Stone theorem for graphs with chromatic number 2 and
o
3.
In this note we will prove a special case of the Erds-Stone theorem, which
o
in full generality completely determines the Turn density for all graphs. A
a
graph H is k-colorable if there exist
Stability for Turns theorem.
a
In this note we prove a version of the classical result of Erds and Simonovits
o
that a graph with no Kt subgraph and a number of edges close to the maximum is close to the extreme example. In particular, such a graph is nea
VAN DER WAERDENS THEOREM
AKOS MAGYAR
An arithmetic progression (AP) of length k is a set of the form A = cfw_a, a+d, . . . , a+(k 1)d
which well also denote by A = a+[0, k 1]d. A basic result due to Van der Waerden in 1927,
says that if the natural number
Combinatorial Nullstellensatz
Noga Alon
Abstract
We present a general algebraic technique and discuss some of its numerous applications in
Combinatorial Number Theory, in Graph Theory and in Combinatorics. These applications include results in additive nu