This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bennett-Wood D, Enting I G, Gaunt D S, Guttmann A J, Leask J L, Owczarek A L and Whittington S G 1998 Exact enumeration study of free energies of interacting polygons and walks in two dimensions J. Phys. A 31 4725–4741
Clisby N, Liang R and Slade G 2007 Self-avoiding walk enumeration via the lace expansion J. Phys. A 40 10973–11017
Conway A R 1995 Enumerating 2D percolation series by the finite lattice method J. Phys. A 28 335–349
Delest M P and Viennot G 1984 Algebraic languages and polyominoes enumeration Theor. Comput. Scie. 34 169–206
Domb C 1960 On the theory of cooperative phenomena in crystals Advances in Physics 9 149–361
Enting I G 1980 Generating functions for enumerating self-avoiding rings on the square lattice J. Phys. A 13 3713–3722
Enting I G 1986 Lattice models of firn closure: I. Percolation on the interstices of the BCC lattice J. Phys. A 19 2841–2854
Enting I G and Guttmann A J 1985 Self-avoiding polygons on the square, L and Manhattan lattices J. Phys. A 18 1007–1017
Enting I G and Guttmann A J 1989 Polygons on the honeycomb lattice J. Phys. A 22 1371–1384
Enting I and Guttmann A 1992 Self-avoiding rings on the triangular lattice J. Phys. A: Math. Gen. 25 2791–2807
Guttmann A J 1989 Asymptotic analysis of power-series expansions in Phase Transitions and Critical Phenomena (eds. C Domb and J L Lebowitz) (New York: Academic) vol. 13 1–234
Guttmann A J and Enting I G 1988 The number of convex polygons on the square and honey-comb lattices J. Phys. A 21 L467–474
Guttmann A J and Enting I G 1988 The size and number of rings on the square lattice J. Phys. A 21 L165–172
Guttmann A J, Jensen I, Wong L H and Enting I G 2000 Punctured polygons and polyominoes on the square lattice J. Phys. A 33 1735–1764
Jensen I 2001 Enumerations of lattice animals and trees J. Stat. Phys. 102 865–881
Jensen I 2003 A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice J. Phys. A 36 5731–5745
Jensen I 2006 Honeycomb lattice polygons and walks as a test of series analysis techniques J. Phys.: Conf. Ser. 42 163–178
Jensen I and Guttmann A J 1999 Self-avoiding polygons on the square lattice J. Phys. A 32 4867–4876
Knuth D E 1969 Seminumerical Algorithms. The Art of Computer Programming, Vol 2. (Read-ing, Mass: Addison Wesley)
MacDonald D, Hunter D L, Kelly K and Jan N 1992 Self-avoiding walks in two to five dimen-sions: exact enumerations and series study J. Phys. A 25 1429–1440
Martin J L 1962 The exact enumeration of self-avoiding walks on a lattice Proc. Camb. Phil. Soc. 58 92–101
Martin J L 1974 Computer techniques for evaluating lattice constants in Phase Transitions and Critical Phenomena (eds. C Domb and M Green) (New York: Academic) vol. 3 97–112
Martin J L 1990 The impact of large-scale computing on lattice statistics J. Stat. Phys. 58 774–779
Privman V and Rudnick J 1985 Size of rings in two dimensions J. Phys. A 18 L789–L793
Rushbrooke G S and Eve J 1959 On noncrossing lattice polygons J. Chem Phys. 31 1333–1334
Rushbrooke G S and Eve J 1962 High-temperature Ising partition function and related non-crossing polygons for the simple cubic lattice J. Math. Phys. 3 185–189
Stanley R P 1999 Enumerative Combinatorics vol. 2 (Cambridge: Cambridge University Press)
Sykes M F, Essam J and Gaunt D S 1965 Derivation of low-temperature expansions for the Ising model of a ferromagnet and an antiferromagnet J. Math. Phys. 6 283–298
Sykes M F 1986 Generating functions for connected embeddings in a lattice: I. Strong embed-dings J. Phys. A 19 1007–1025
Sykes M F 1986 Generating functions for connected embeddings in a lattice: II. Weak embed-dings in a lattice: II. Weak embeddings J. Phys. A 19 1027–1032
Sykes M F 1986 Generating functions for connected embeddings in a lattice: III. Bond perco-lation in a lattice: III. Bond percolation J. Phys. A 19 2425–2429
Sykes M F 1986 Generating functions for connected embeddings in a lattice: IV. Site perco-lation J. Phys. A 19 2431–2437
Sykes M F and Wilkinson M K 1986 Generating functions for connected embeddings in a lattice: V. Application to the simple cubic and body-centred cubic lattice J. Phys. A 19 3407–3414
Sykes M F and Wilkinson M K 1986 Derivation of series expansions for a study of percolation processes J. Phys. A 19 3415–3424
Torrie G and Whittington S G 1975 Exact enumeration of neighbour-avoiding walks on the tetrahedral and body-centred cubic lattices J. Phys. A 8 1178–1184
Vöge M, Guttmann A J and Jensen I 2002 On the number of benzenoid hydrocarbons J. Chem. Inf. Comput. Sci. 42 456–466
Vöge M and Guttmann A 2003 On the number of hexagonal polyominoes Theo. Comp. Sci. 307 433–453
Wakefield A J 1951 Statistics of the simple cubic lattice Proc. Camb. Phil. Soc. 47 419–435 and 799–810
Wortis M F 1974 Linked cluster expansions in Phase Transitions and Critical Phenomena (eds. C Domb and M Green) (New York: Academic) vol. 3 114–180
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Canopus Academic Publishing Limited
About this chapter
Cite this chapter
Enting, I.G., Jensen, I. (2009). Exact Enumerations. In: Guttman, A.J. (eds) Polygons, Polyominoes and Polycubes. Lecture Notes in Physics, vol 775. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9927-4_7
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9927-4_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9926-7
Online ISBN: 978-1-4020-9927-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)