Une bijection entre les polyominos convexes dirigés et les mots de Dyck bilatères

M. Bousquet-Mélou

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1992)

  • Volume: 26, Issue: 3, page 205-219
  • ISSN: 0988-3754

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Bousquet-Mélou, M.. "Une bijection entre les polyominos convexes dirigés et les mots de Dyck bilatères." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 26.3 (1992): 205-219. <http://eudml.org/doc/92415>.

@article{Bousquet1992,
author = {Bousquet-Mélou, M.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {bilateral Dycle language; methodology; algebraic language},
language = {fre},
number = {3},
pages = {205-219},
publisher = {EDP-Sciences},
title = {Une bijection entre les polyominos convexes dirigés et les mots de Dyck bilatères},
url = {http://eudml.org/doc/92415},
volume = {26},
year = {1992},
}

TY - JOUR
AU - Bousquet-Mélou, M.
TI - Une bijection entre les polyominos convexes dirigés et les mots de Dyck bilatères
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 1992
PB - EDP-Sciences
VL - 26
IS - 3
SP - 205
EP - 219
LA - fre
KW - bilateral Dycle language; methodology; algebraic language
UR - http://eudml.org/doc/92415
ER -

References

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  1. [Ba l] R. BAXTER, Hard hexagons: exact solution, J. Phys. A: Math. Gen., 1980, 13, L 61-L 70. MR560533
  2. [Ba 2] R. BAXTER, Exactly solved models in statistical mechanics, Academic Press, New-York, 1982. Zbl0538.60093MR690578
  3. [Bo-Vi] M. BOUSQUET-MÉLOU et X. G. VIENNOT, Empilements de segments et q-énumération de polyominos convexes dirigés, à paraître dans J. Comb. Th. Series A. Zbl0753.05023
  4. [De-Du] M. P. DELEST et S. DULUCQ, Enumeration of directed column-convex animals with given perimeter and area, Rapport n° 86-15, Université Bordeaux-I, soumis à publication. 
  5. [De-Vi] M. P. DELEST et X. G. VIENNOT, Algebraic languages and polyominoes enumeration, Theor. Comp. Sci., 1984, 34, p. 169-206, North-Holland. Zbl0985.68516
  6. [De-Na-Va] B. DERRIDA, J. P. NADAL et J. VANNIMENUS, Directed lattices animals in 2 dimensions: numerical and exact relults, J. Phys, 1982, 43, p. 1561. 
  7. [Dh1] D. DHAR, Equivalence of the two-dimensional directede animal problem to Baxter hard-square lattice-gas model, Phys. Rev. Lett., 1982, 49, p. 959-962. 
  8. [Dh 2] D. DHAR, Exact solution of a directed-site animals enumeration in 3 dimensions, Phys. Rev. Lett., 1983, 59, p. 853-856. 
  9. [Fe] J. M. FEDOU, Exact formulas for fully compact animals, Rapport LaBRI n° 89-06, Université Bordeaux-I. 
  10. [Ga] M. GARDNER, Mathematical games, Scientific American, 1958, sept. 182-192, nov. 136-142. 
  11. [Go] S. GOLOMB, Polyominoes, Scribner, New York, 1965. 
  12. [Go-Vi] D. GOUYOU-BEAUCHAMPS et X. G. VIENNOT, Equivalence of the two dimensional directed animal problem to a one-dimensional path problem, Adv. in Appl. Math., 1988, 9, p. 334-357. Zbl0727.05036
  13. [Ha-Na] V. HAKIM et J. P. NADAL, Exact resuit for 2 D directed lattice animais on a strip of finite width, J. Phys. A: Math. Gen., 1983, 16, L 213-L 218. 
  14. [Kl-Ri] D. A. KLARNER et R. L. RIVEST, A procedure for improving the upper bound for the number of n-ominoes, Can. J. Math, 1973, 25, p. 585-602. Zbl0261.05113MR323587
  15. [Li-Ch] K. Y. LIN et S. J. CHANG, Rigourous results for the number of convex polygons on the square and honeycomb lattices, J. Phys. A: Math. Gen., 1988, 21, p. 2635-2642. MR953200
  16. [Pe 1] J. G. PENAUD, Une nouvelle bijection pour les animaux dirigés, Rapport LaBRI n° 89-45, Université Bordeaux-I, Actes du 22e Séminaire Lotharingien de Combinatoire, Hesselberg, 1989, p. 93-130. 
  17. [Pe 2] J. G. PENAUD, Animaux dirigés diagonalement convexes et arbres ternaires, Rapport LaBRI n° 90-62, Université Bordeaux-I. 
  18. [Pe 3] J. G. PENAUD, Arbres et Animaux, Mémoire d'habilitation à diriger les recherches, Université Bordeaux-I, mai 1990. 
  19. [Pr-Fo] V. PRIVMAN et G. FORGACS, Exact solution of the partially directed compact lattice animal model, J. Phys. A: Math. Gen., 1987, 20, p. 543-547. MR893296
  20. [Pr-Sv] V. PRIVMAN et N. M. SVRAKIC, Exact generating fucntion for fully directed compact lattice animals, Phys. Rev. Lett., 1988, 60, n° 12, p. 1107-1109. MR932171
  21. [Vi] X. G. VIENNOT, Problèmes combinatoires posés par la physique statistique, Séminaire Bourbaki, n° 626, 36e année, in Astérisque, n° 121-122, 1985, p. 225-246, Soc. Math. France. Zbl0563.60095MR768962

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