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Publication type: Journal

We introduce and study the combinatorial optimization problem with interaction costs (COPIC). COPIC is the problem of finding two combinatorial structures, one from each of two given families, such that the sum of their independent linear costs and the interaction costs between elements of the two selected structures is minimized. COPIC generalizes the quadratic assignment […]

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Publication type: Journal

Let $\ac(n,k)$ denote the smallest positive integer with the property that there exists an $n$-colouring $f$ of $\{1,\dots,\ac(n,k)\}$ such that for every $k$-subset $R \subseteq \{1, \dots, n\}$ there exists an (arithmetic) $k$\nobreakdash-progression $A$ in $\{1,\dots,\ac(n,k)\}$ with $\{f(a) : a \in A\} = R$. Determining the behaviour of the function $\ac(n,k)$ is a previously unstudied […]

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