### On the maximum number of integer colourings with forbidden monochromatic sums

Combinatorics Seminar

28th November 2017, 11:00 am – 12:00 pm

Howard House, 4th Floor Seminar Room

Let $f(n,r)$ denote the maximum number of colourings of $A \subseteq \{1,\ldots,n\}$ with $r$ colours such that each colour class is sum-free.

Here, a sum is a subset $\{x,y,z\}$ such that $x+y=z$. We show that $f(n,2) = 2^{\lceil n/2\rceil}$, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of $f(n,r)$ for $r \leq 5$.

This is joint work with Hong Liu and Katherine Staden.

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