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Algorithms, Combinatorics and Optimization Seminar
For more information, please visit the home page for the program in Algorithms, Combinatorics and Optimization at Carnegie Mellon University. Carnegie Mellon University offers an interdisciplinary Ph.D program in Algorithms, Combinatorics and Optimization. This program is the first of its kind in the United States. It is administered jointly by the Tepper School of Business (Operations Research group), the Computer Science Department (Algorithms and Complexity group) and the Department of Mathematical Sciences (Discrete Mathematics group). (Learn more...) Ben Barber University of Cambridge Title: Partition regularity in the rationals Abstract: A system of linear equations with integer coefficients is partition regular if, whenever the natural numbers are finitely coloured, it has a monochromatic solution. Rado gave a good characterisation of the finite partition regular systems, but even examples of infinite partition regular systems are hard to find. I will describe a new family of infinite partition regular systems, and how it can be used to answer a long-standing open question: if a system of equations is partition regular over the rationals, must it also be partition regular over the natural numbers? Joint work with Neil Hindman and Imre Leader. |