Cohen, G. L.; Tonkes, E. Dartboard arrangements. (English) Zbl 0981.05003 Electron. J. Comb. 8, No. 2, Research Paper R4, 8 p. (2001). Summary: This note considers possible arrangements of the sectors of a generalised dartboard. The sum of the \(p\)th powers of the absolute differences of the numbers on adjacent sectors is introduced as a penalty cost function and a string reversal algorithm is used to determine all arrangements that maximise the penalty, for any \(p\geq 1\). The maximum value of the penalty function for \(p=1\) is well known in the literature, and has been previously stated without proof for \(p=2\). We determine it also for \(p=3\) and \(p=4\). Cited in 2 Documents MSC: 05A05 Permutations, words, matrices Keywords:arrangements; dartboard; penalty function PDFBibTeX XMLCite \textit{G. L. Cohen} and \textit{E. Tonkes}, Electron. J. Comb. 8, No. 2, Research paper R4, 8 p. (2001; Zbl 0981.05003) Full Text: EuDML EMIS