Geodesic
New lower bounds for Heilbronn numbers
The electronic journal of combinatorics, Tome 9 (2002)
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The $n$-th Heilbronn number, $H_n$, is the largest value such that $n$ points can be placed in the unit square in such a way that all possible triangles defined by any three of the points have area at least $H_n$. In this note we establish new bounds for the first Heilbronn numbers. These new values have been found by using a simple implementation of simulated annealing to obtain a first approximation and then optimizing the results by finding the nearest exact local maximum.
DOI : 10.37236/1623
Classification : 52C35, 52A40, 51M25
Mots-clés : Heilbronn numbers, combinatorics, simulated annealing 
@article{10_37236_1623,
     author = {Francesc Comellas and J. Luis A. Yebra},
     title = {New lower bounds for {Heilbronn} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1623},
     zbl = {1008.52020},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1623/}
}
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%A J. Luis A. Yebra
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Francesc Comellas; J. Luis A. Yebra. New lower bounds for Heilbronn numbers. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1623

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