##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Steve Butler

#### UCLA

## Finding patterns that do not contain many monochromatic constellations

##### Abstract:

Fix some set of points. Then a constellation in [n] is a scaled translated copy of the points. Given a 2-coloring of [n] there must be some monochromatic copies of any fixed constellation (assuming n is sufficiently large). In this paper we outline a method to experimentally find a block coloring of [n] that avoids many monochromatic copies of the constellation. We also show that for constellations with three points we can always beat random coloring. (Joint work with Kevin Costello (Georgia Tech.) and Ron Graham (UCSD).)

Host: Jeff Remmel

### January 12, 2010

### 3:00 PM

### AP&M 7141

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