Tilings and isoperimetrical shapes I: Square lattice

Sylvain Gravier; Charles Payan

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

  • Volume: 40, Issue: 1, page 63-77
  • ISSN: 0231-9721

How to cite

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Gravier, Sylvain, and Payan, Charles. "Tilings and isoperimetrical shapes I: Square lattice." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 40.1 (2001): 63-77. <http://eudml.org/doc/23720>.

@article{Gravier2001,
author = {Gravier, Sylvain, Payan, Charles},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {tilings with optimal polyominos; maximizing the area for a given perimeter; isoperimetrical inequality; Pentomino Exclusion Problem; isoperimetrical shapes; optimal shapes; Colomb type problem},
language = {eng},
number = {1},
pages = {63-77},
publisher = {Palacký University Olomouc},
title = {Tilings and isoperimetrical shapes I: Square lattice},
url = {http://eudml.org/doc/23720},
volume = {40},
year = {2001},
}

TY - JOUR
AU - Gravier, Sylvain
AU - Payan, Charles
TI - Tilings and isoperimetrical shapes I: Square lattice
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2001
PB - Palacký University Olomouc
VL - 40
IS - 1
SP - 63
EP - 77
LA - eng
KW - tilings with optimal polyominos; maximizing the area for a given perimeter; isoperimetrical inequality; Pentomino Exclusion Problem; isoperimetrical shapes; optimal shapes; Colomb type problem
UR - http://eudml.org/doc/23720
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. Golomb S. W., Polyominoes - Puzzles, Patterns, Problems, and Packings, Princeton Science Library, 1994. (1994) Zbl0831.05020MR1291821
  6. Melissen H., Packing and Covering with Circles, PhD Thesis, Proefschrift Universiteit Utrecht, Nederland, 1997. (1997) 
  7. 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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