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On the maximum number of integer colourings with forbidden monochromatic sums
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. Similar results were obtained by Hán and Jiménez in the setting of finite abelian groups.
On the maximum number of integer colourings with forbidden monochromatic sums
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. Similar results were obtained by Hán and Jiménez in the setting of finite abelian groups.
On the maximum number of integer colourings with forbidden monochromatic sums
Liu, Hong (author) / Sharifzadeh, Maryam (author) / Staden, Katherine (author)
2021-01-01
ISI:000652332700001
Article (Journal)
Electronic Resource
English
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