[Discrete-math-seminar] IIT Discrete Math Seminar, Wed 4:30pm

[Hemanshu Kaul]

Hello all,

This week Kevin Ventullo, an undergraduate student at IIT, will talk
about some Ramsey properties of integers including his research from
last year. The talk should be accessible to most students, especially
those who have seen even a little bit of combinatorics/graph theory. So
all students are strongly encouraged to attend the talk.

We will meet at 4:30pm on Wednesday at the usual seminar room - 245 in
E1 building.

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Some Ramsey Properties of the Integers

Kevin Ventullo
Illinois Institute of Technology

Wednesday, 9th April, 2008, E1 245, 4:30 pm

Given a set of integers D, a D-diffsequence is a combinatorial object
closely related to arithmetic progressions. It is defined to be any
sequence a(1), a(2), ..., a(n) such that the consecutive differences
(a(i) - a(i-1)) are in D for all 
2 < i < n.

The degree of accessibility of a set D, denoted doa(D), is defined to be
the greatest integer r such that every r-coloring of positive integers
contains arbitrarily long monochromatic D-diffsequences. We will
introduce and discuss 
some elementary properties and examples for these and other Ramsey-type
concepts 
in a way that should be accessible to most undergraduates.

Our main result will be a new upper bound on doa(P+c), where P+c denotes
the 
set of prime numbers translated by a constant c > 1.
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I hope to see you all there.

Hemanshu


Hemanshu Kaul
Assistant Professor of Applied Mathematics
Illinois Institute of Technology, Chicago
http://www.math.iit.edu/~kaul/