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LIMDA Joint Seminar Announcement

Christoph Spiegel (Freie Universität Berlin): Threshold functions for systems of equations in random sets

Quan
17/03/2016 des de/d' 12:00"
On
Room C3-005, Campus Nord UPC
iCal

Abstract

We present a unified framework to deal with threshold functions for the existence of solutions to systems of linear equations in random sets. This covers the study of several fundamental combinatorial families such as k-arithmetic progressions, k-sum-free sets, B_h(g)- sequences and Hilbert cubes of dimension k.

We show that there exists a threshold function for the property "A^m contains a non-trivial solution of Mx=0" where A is a random set. This threshold function depends on a parameter maximized over all subsystems, a notion previously introduced by Rödl and Rucinski. The talk will contain a formal definition of trivial solutions for any combinatorial structure, extending a previous definition by Ruzsa.

Joint work with Juanjo Rué Perna and Ana Zumalacárregui.