Formulae and growth rates of high-dimensional polycubes

Combinatorica

Volumn 30, Issue 3, 2010, Pages 257-275

  Barequet, Ronnie ^a   Barequet, Gill ^b   Rote, Günter ^c  

^a TEL AVIV UNIVERSITY   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957158262     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00493-010-2448-8     Document Type: Article

References (24)

1. G. Aleksandrowicz and G. Barequet: Counting d-dimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications19(3) (2009), 215-229.
2. G. Aleksandrowicz and G. Barequet: Counting polycubes without the dimensionality curse, Discrete Mathematics309(13) (2009), 4576-4583.
3. G. Barequet, M. Moffie, A. Ribó and G. Rote: Counting polyominoes on twisted cylinders, Integers (electronic journal) 6 (2006), #A22, 37 pp.
4. S. R. Broadbent and J. M. Hammersley: Percolation processes: I. Crystals and mazes; Proc. Cambridge Philosophical Society53 (1957), 629-641.
5. M. Eden: A two-dimensional growth process, in: Proc. 4th Berkeley Symp. on Mathematical Statistics and Probability, IV, Berkeley, CA, pp. 223-239, 1961.
6. D. S. Gaunt: The critical dimension for lattice animals, J. of Physics A: Mathematical and General13 (1980), L97-L101.
7. D. S. Gaunt and P. J. Peard: 1/d-expansions for the free energy of weakly embedded site animal models of branched polymers, J. of Physics A: Mathematical and General33 (2000), 7515-7539.
8. D. S. Gaunt, P. J. Peard, C. E. Soteros and S. G. Whittington: Relationships between growth constants for animals and trees, J. of Physics A: Mathematical and General27 (1994), 7343-7351.
9. D. S. Gaunt, M. F. Sykes and H. Ruskin: Percolation processes in d-dimensions, J. of Physics A: Mathematical and General9 (1976), 1899-1911.
10. T. Hara and G. Slade: The self-avoiding-walk and percolation critical points in high dimensions, Combinatorics, Probability, and Computing4 (1995), 197-215.
11. I. Jensen: Counting polyominoes: A parallel implementation for cluster computing; in: Proc. Int. Conf. on Computational Science, part III, Melbourne, Australia and St. Petersburg, Russia, Lecture Notes in Computer Science2659, Springer, pp. 203-212, June 2003.
12. D. A. Klarner: Cell growth problems, Canadian J. of Mathematics19 (1967), 851-863.
13. D. A. Klarner and R. L. Rivest: A procedure for improving the upper bound for the number of n-ominoes, Canadian J. of Mathematics25 (1973), 585-602.
14. W. F. Lunnon: Symmetry of cubical and general polyominoes, in: Graph Theory and Computing (R. C. Read, ed.), Academic Press, New York, pp. 101-108, 1972.
15. W. F. Lunnon: Counting multidimensional polyominoes, The Computer Journal18 (1975), 366-367.
16. N. Madras: A pattern theorem for lattice clusters, Annals of Combinatorics3 (1999), 357-384.
17. N. Madras, C. E. Soteros, S. G. Whittington, J. L. Martin, M. F. Skeys, S. Flesia and D. S. Gaunt: The free energy of a collapsing branched polymer, J. of Physics A: Mathematical and General23 (1990), 5327-5350.
18. J. L. Martin: The impact of large-scale computing on lattice statistics, J. of Statistical Physics58 (1990), 749-774.
19. J. W. Moon: Counting Labelled Trees, Canadian Mathematical Monographs, no. 1, Wiliam Clowes & Sons, London and Beccles, 1970.
20. P. J. Peard and D. S. Gaunt: 1/d-expansions for the free energy of lattice animal models of a self-interacting branched polymer, J. of Physics A: Mathematical and General28 (1995), 6109-6124.
21. D. H. Redelmeier: Counting polyominoes: Yet another attack; Discrete Mathematics36 (1981), 191-203.
22. M. Schwartz and T. Etzion: Two-dimensional cluster-correcting codes, IEEE Trans. on Information Theory51 (2005), 2121-2132.
23. N. J. A. Sloane: The on-line encyclopedia of integer sequences, available at http: //www. research. att. com/~njas/sequences.
24. S. Whittington and C. Soteros: Lattice animals: Rigorous results and wild guesses; in: Disorder in Physical Systems (G. Grimmett and D. Welsh, eds.), Clarendon Press, Oxford, pp. 323-335, 1990.