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Speaker:

Amanda Montejano
Affiliation:

National Autonomous University of Mexico
Date:

Wed, 2017-06-28 14:15 - 15:15
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar Zero-sum Ramsey theory is a newly established area in combinatorial number theory. Zero-sum problems can be formulated as follows: If the elements of a combinatorial structure are mapped into a finite group $\Gamma$, does there exists a prescribed substructure, such that the sum of the weights of its elements is the neutral element of $\Gamma$? Extending classical results in zero-sum Ramsey theory, we study mappings to a set of integers $\{-r, \cdots ,0, \cdots ,r\}$ seeking zero-sum subsets. We will focus in two types of structures, namely complete graphs and intervals of integers. Relying heavily on Pell equations and some classical biquadratic Diophantine equations, we solve an open problem formulated by Caro and Yuster and supply a good understanding of the situation concerning the complete graph $K_4$. This is a joint work with Yair Caro and Adriana Hansberg.

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