On the maximum number of integer colourings with forbidden monochromatic sums

Hong Liu

Mathematics Institute, University of Warwick, Warwick, UK

Mathematics Institute, University of Warwick, Warwick, UK

2017/12/27 Wed 4PM-5PM (Room 3433)

Let f(n,r) denote the maximum number of colourings of A⊆{1,…,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

Joint work with Maryam Sharifzadeh and Katherine Staden.

^{⌈n/2⌉}, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of f(n,r) for r≤5.Joint work with Maryam Sharifzadeh and Katherine Staden.

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