Geodesic
Dartboard arrangements
The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2
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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 $p\ge1$. 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 $p=4$.
DOI : 10.37236/1603
Classification : 05A05
Mots-clés : arrangements, dartboard, penalty function 
@article{10_37236_1603,
     author = {G. L. Cohen and E. Tonkes},
     title = {Dartboard arrangements},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {2},
     doi = {10.37236/1603},
     zbl = {0981.05003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1603/}
}
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G. L. Cohen; E. Tonkes. Dartboard arrangements. The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2. doi: 10.37236/1603

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