On sequences covering all rainbow $k$-progressions

Leonardo Alese, Stefan Lendl, Paul Tabatabai
2018 Journal of Combinatorics  
Let ac(n, k) denote the smallest positive integer with the property that there exists an n-colouring f of {1, . . . , ac(n, k)} such that for every k-subset R ⊆ {1, . . . , n} there exists an (arithmetic) Determining the behaviour of the function ac(n, k) is a previously unstudied problem. We use the first moment method to give an asymptotic upper bound for ac(n, k) for the case k = o(n 1/5 ).
doi:10.4310/joc.2018.v9.n4.a9 fatcat:wc5uadytojff5envzeabq4jaya