Tilings and isoperimetrical shapes. II. Hexagonal lattice

Sylvain Gravier

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2001)

  • Volume: 40, Issue: 1, page 79-92
  • ISSN: 0231-9721

How to cite

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Gravier, Sylvain. "Tilings and isoperimetrical shapes. II. Hexagonal lattice." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 40.1 (2001): 79-92. <http://eudml.org/doc/23702>.

@article{Gravier2001,
author = {Gravier, Sylvain},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {minimizing the area for a given perimeter; tiling; polyhexe; isoperimetrical inequality; hexagonal lattice; graphs; optimal shapes; polyominoes on the honeycomb lattice; minimum density of unit hexagon; Colomb type problem},
language = {eng},
number = {1},
pages = {79-92},
publisher = {Palacký University Olomouc},
title = {Tilings and isoperimetrical shapes. II. Hexagonal lattice},
url = {http://eudml.org/doc/23702},
volume = {40},
year = {2001},
}

TY - JOUR
AU - Gravier, Sylvain
TI - Tilings and isoperimetrical shapes. II. Hexagonal lattice
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2001
PB - Palacký University Olomouc
VL - 40
IS - 1
SP - 79
EP - 92
LA - eng
KW - minimizing the area for a given perimeter; tiling; polyhexe; isoperimetrical inequality; hexagonal lattice; graphs; optimal shapes; polyominoes on the honeycomb lattice; minimum density of unit hexagon; Colomb type problem
UR - http://eudml.org/doc/23702
ER -

References

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  1. Alonso L., Cerf R., The three dimensional polyominoes of minimal area, Electronic J. of Combin. 3 (1996), 1-39. (1996) Zbl0885.05056MR1410882
  2. Bollobás B., Leader I., Compressions and Isoperimetric Inequalities, J. Combin. Theory Ser. A 56 (1991), 47-62. (1991) Zbl0731.05043MR1082842
  3. Bosch R. A., A Pentomino Exclusion Problem, Mathematical Programming Newsletter, Optima 60 (december 1998), 3. (1998) 
  4. Bosch R. A., Peaceably Coexisting Armies of Queens, Mathematical Programming Newsletter, Optima 62 (June 1999), 3. (1999) MR1244056
  5. Conway J. H., Sloane N. J. A., Sphere Packings, Lattices and Groups, Springer-Verlag, 1996. (1996) 
  6. Golomb S. W., Polyominoes -Puzzles, Patterns, Problems, and Packings, Princeton Science Library, 1994. (1994) Zbl0831.05020MR1291821
  7. Gravier S., Payan, C, Tilings and Isoperimetrical Shapes I: Square lattice, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 40 (2001), 57-71. Zbl1042.52019MR1904686
  8. Gravier S., Payan, C, Pentomino Exclusion Problem, Disc. and Comput. Geom., (1999), (to appear). (1999) MR1854107
  9. Melissen H., Packing and Covering with Circles, PhD Thesis, Proefschrift Universiteit Utrecht, Nederland, 1997. (1997) 
  10. Wang D.-L., Wang P., Extremal configurations on a discrete torus and a generalization of the generalized Macaulay theorem, SIAM J. Appl. Math. 33 (1977), 55-59. (1977) Zbl0362.05048MR0438237

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