Monochromatic configurations in finite colorings of N
 
 
Description:  Is it possible to color the natural numbers with finitely many colors, so that whenever x and y are of the same color, their sum x+y has a different color? A 1916 theorem of I. Schur tells us that the answer is *no*. In other words, for any finite coloring of N, there exist x and y such that the triple {x,y,x+y} is *monochromatic* (i.e. has all terms have the same color). A similar result holds if one replaces the sum x+y with the product xy, however, it is still unknown whether one can finitely color the natural numbers in a way that no quadruple {x,y,x+y,xy} is monochromatic! In this talk I will present a recent partial solution to this problem, showing that any finite coloring of the natural numbers yields a monochromatic triple {x,x+y,xy}.
Date:  2016-07-06
Start Time:   15:00
Speaker:  Joel Moreira (Ohio State Univ., USA)
Institution:  Ohio State University
Place:  Room 5.5 DMUC
Research Groups: -Algebra and Combinatorics
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