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On the maximum number of integer colourings with forbidden monochromatic sums
[2017 Discrete Math 세미나]
Date: 2017-12-27
Speaker : Hong Liu (University of Warwick, Warwick, UK)
Abstract : 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^(⌈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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