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Volumn 126, Issue 3, 2007, Pages 649-667

Spanning trees on the Sierpinski gasket

Author keywords

Exact solutions; Sierpinski gasket; Spanning trees

Indexed keywords


EID: 33847185591     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9262-0     Document Type: Article
Times cited : (111)

References (37)
  • 1
    • 4944257625 scopus 로고
    • Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Ströme geführt wird
    • G. Kirchhoff, Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Ströme geführt wird. Ann. Phys. Chem. 72:497-508 (1847).
    • (1847) Ann. Phys. Chem , vol.72 , pp. 497-508
    • Kirchhoff, G.1
  • 2
    • 0004242420 scopus 로고
    • 2nd edn, Cambridge University Press, Cambridge
    • N. L. Biggs, Algebraic Graph Theory, 2nd edn. (Cambridge University Press, Cambridge, 1993).
    • (1993) Algebraic Graph Theory
    • Biggs, N.L.1
  • 3
    • 0003238314 scopus 로고
    • Complexity: Knots, Colourings, and Counting
    • Cambridge University Press, Cambridge
    • D. J. A. Welsh, Complexity: Knots, Colourings, and Counting (London Math. Soc. Lecture Notes series 186). (Cambridge University Press, Cambridge, 1993).
    • (1993) London Math. Soc. Lecture Notes series , vol.186
    • Welsh, D.J.A.1
  • 4
    • 0001716571 scopus 로고
    • Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances
    • R. Burton and R. Pemantle, Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances. Ann. Probab. 21:1329-1371 (1993).
    • (1993) Ann. Probab , vol.21 , pp. 1329-1371
    • Burton, R.1    Pemantle, R.2
  • 5
    • 23844524256 scopus 로고    scopus 로고
    • Asymptotic enumeration of spanning trees
    • R. Lyons, Asymptotic enumeration of spanning trees, Combin. Probab. Comput. 14:491-522 (2005).
    • (2005) Combin. Probab. Comput , vol.14 , pp. 491-522
    • Lyons, R.1
  • 6
    • 33847238948 scopus 로고    scopus 로고
    • H. N. V. Temperley, in: Combinatorics: Proc. Combinatorial Mathematics, D. J. A. Welsh and D. R. Woodall, editors. (The Institute of Mathematics and its Applications, Oxford, 1972, pp. 356-357).
    • H. N. V. Temperley, in: Combinatorics: Proc. Combinatorial Mathematics, D. J. A. Welsh and D. R. Woodall, editors. (The Institute of Mathematics and its Applications, Oxford, 1972, pp. 356-357).
  • 7
    • 0000033790 scopus 로고
    • Number of spanning trees on a lattice
    • F.-Y. Wu, Number of spanning trees on a lattice, J. Phys. A: Math. Gen. 10:L113-L115 (1977).
    • (1977) J. Phys. A: Math. Gen , vol.10
    • Wu, F.-Y.1
  • 8
    • 0041855748 scopus 로고
    • On the random cluster model. I. Introduction and relation to other models
    • C. M. Fortuin and P. W. Kasteleyn, On the random cluster model. I. Introduction and relation to other models. Physica 57:536-564 (1972).
    • (1972) Physica , vol.57 , pp. 536-564
    • Fortuin, C.M.1    Kasteleyn, P.W.2
  • 9
    • 0042492825 scopus 로고
    • The Potts model
    • F.-Y. Wu, The Potts model, Rev. Mod. Phys. 54:235-268 (1982).
    • (1982) Rev. Mod. Phys , vol.54 , pp. 235-268
    • Wu, F.-Y.1
  • 10
    • 33745657432 scopus 로고    scopus 로고
    • Theoretical studies of self-organized criticality
    • D. Dhar, Theoretical studies of self-organized criticality. Physica A 369:29-70 (2006).
    • (2006) Physica A , vol.369 , pp. 29-70
    • Dhar, D.1
  • 12
    • 0000170712 scopus 로고
    • Combinatorics
    • T. P. McDonough and V. C. Mavron, editors, Cambridge University Press, Cambridge
    • H. N. V. Temperley, Combinatorics (London Math. Soc. Lecture Note Series #13), T. P. McDonough and V. C. Mavron, editors. (Cambridge University Press, Cambridge, 1974, pp. 202-204).
    • (1974) London Math. Soc. Lecture Note Series , vol.13 , pp. 202-204
    • Temperley, H.N.V.1
  • 13
    • 0002374912 scopus 로고    scopus 로고
    • Spanning trees on hypercubic lattices and nonorientable surfaces
    • W.-J. Tzeng and F.-Y. Wu, Spanning trees on hypercubic lattices and nonorientable surfaces. Appl. Math. Lett. 13:19-25 (2000).
    • (2000) Appl. Math. Lett , vol.13 , pp. 19-25
    • Tzeng, W.-J.1    Wu, F.-Y.2
  • 14
    • 0034595456 scopus 로고    scopus 로고
    • Spanning trees on graphs and lattices in d dimensions
    • R. Shrock and F.-Y. Wu, Spanning trees on graphs and lattices in d dimensions. J. Phys. A: Math. Gen. 33:3881-3902 (2000).
    • (2000) J. Phys. A: Math. Gen , vol.33 , pp. 3881-3902
    • Shrock, R.1    Wu, F.-Y.2
  • 15
    • 33646399152 scopus 로고    scopus 로고
    • Some exact results for spanning trees on lattices
    • S.-C. Chang and R. Shrock, Some exact results for spanning trees on lattices. J. Phys. A: Math. Gen. 39:5653-5658 (2006).
    • (2006) J. Phys. A: Math. Gen , vol.39 , pp. 5653-5658
    • Chang, S.-C.1    Shrock, R.2
  • 16
    • 33746880684 scopus 로고    scopus 로고
    • Spanning trees on lattices and integral identities
    • S.-C. Chang and W. Wang, Spanning trees on lattices and integral identities. J. Phys. A: Math. Gen. 39:10263-10275 (2006).
    • (2006) J. Phys. A: Math. Gen , vol.39 , pp. 10263-10275
    • Chang, S.-C.1    Wang, W.2
  • 20
    • 0000802793 scopus 로고
    • Solvable fractal family, and its possible relation to the backbone at percolation
    • Y. Gefen and A. Aharony, Solvable fractal family, and its possible relation to the backbone at percolation. Phys. Rev. Lett. 47:1771-1774 (1981).
    • (1981) Phys. Rev. Lett , vol.47 , pp. 1771-1774
    • Gefen, Y.1    Aharony, A.2
  • 21
    • 0001502928 scopus 로고
    • Spectrum of the Schrödinger equation on a self-similar structure
    • R. Rammal and G. Toulouse, Spectrum of the Schrödinger equation on a self-similar structure. Phys. Rev. Lett. 49:1194-1197 (1982).
    • (1982) Phys. Rev. Lett , vol.49 , pp. 1194-1197
    • Rammal, R.1    Toulouse, G.2
  • 22
    • 0001534008 scopus 로고
    • Superconductivity of networks. A percolation approach to the effects of disorder
    • S. Alexander, Superconductivity of networks. A percolation approach to the effects of disorder. Phys. Rev. B 27:1541-1557 (1983).
    • (1983) Phys. Rev. B , vol.27 , pp. 1541-1557
    • Alexander, S.1
  • 23
    • 0000272107 scopus 로고
    • Solutions to the Schrödinger equation on some fractal lattices
    • E. Domany, S. Alexander, D. Bensimon and L. P. Kadanoff, Solutions to the Schrödinger equation on some fractal lattices. Phys. Rev. B 28:3110-3123 (1983).
    • (1983) Phys. Rev. B , vol.28 , pp. 3110-3123
    • Domany, E.1    Alexander, S.2    Bensimon, D.3    Kadanoff, L.P.4
  • 24
    • 0001532780 scopus 로고
    • Phase transitions on fractals: I. Quasi-linear lattices
    • Y. Gefen, A. Aharony and B. B. Mandelbrot, Phase transitions on fractals: I. Quasi-linear lattices. J. Phys. A: Math. Gen. 16:1267-1278 (1983);
    • (1983) J. Phys. A: Math. Gen , vol.16 , pp. 1267-1278
    • Gefen, Y.1    Aharony, A.2    Mandelbrot, B.B.3
  • 26
    • 0000241121 scopus 로고
    • Phase transitions on fractals: III. Infinitely ramified lattices
    • Y. Gefen, A. Aharony, and B. B. Mandelbrot, Phase transitions on fractals: III. Infinitely ramified lattices, ibid. 17:1277-1289 (1984).
    • (1984) J. Phys. A: Math. Gen , vol.17 , pp. 1277-1289
    • Gefen, Y.1    Aharony, A.2    Mandelbrot, B.B.3
  • 27
    • 0000390701 scopus 로고
    • Diffusion on the Sierpinski gaskets: A random walker on a fractally structured object
    • R. A. Guyer, Diffusion on the Sierpinski gaskets: A random walker on a fractally structured object. Phys. Rev. A 29:2751-2755 (1984).
    • (1984) Phys. Rev. A , vol.29 , pp. 2751-2755
    • Guyer, R.A.1
  • 29
    • 0002365536 scopus 로고
    • The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket
    • T. Hattori and S. Kusuoka, The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket, ibid. 93:273-284 (1992).
    • (1992) Probab. Theory Relat. Fields , vol.93 , pp. 273-284
    • Hattori, T.1    Kusuoka, S.2
  • 30
    • 0000568139 scopus 로고    scopus 로고
    • Distribution of sizes of erased loops for loop-erased random walks
    • D. Dhar and A. Dhar, Distribution of sizes of erased loops for loop-erased random walks. Phys. Rev. E 55:R2093-R2096 (1997).
    • (1997) Phys. Rev. E , vol.55
    • Dhar, D.1    Dhar, A.2
  • 31
    • 0032141466 scopus 로고    scopus 로고
    • Sandpiles on a Sierpinski gasket
    • F. Daerden and C. Vanderzande, Sandpiles on a Sierpinski gasket. Physica A 256:533-546 (1998).
    • (1998) Physica A , vol.256 , pp. 533-546
    • Daerden, F.1    Vanderzande, C.2
  • 32
    • 37649032418 scopus 로고    scopus 로고
    • Branched polymers on the Given-Mandelbrot family of fractals
    • D. Dhar, Branched polymers on the Given-Mandelbrot family of fractals. Phys. Rev. E 71:031801 (2005).
    • (2005) Phys. Rev. E , vol.71 , pp. 031801
    • Dhar, D.1
  • 33
    • 0003780715 scopus 로고
    • Addison-Wesley, New York
    • F. Harary, Graph Theory (Addison-Wesley, New York, 1969).
    • (1969) Graph Theory
    • Harary, F.1
  • 34
    • 0007012366 scopus 로고
    • Spanning trees in regular graphs
    • B. McKay, Spanning trees in regular graphs. Eur. J. Combin. 4:149-160 (1983).
    • (1983) Eur. J. Combin , vol.4 , pp. 149-160
    • McKay, B.1
  • 35
    • 0002267352 scopus 로고    scopus 로고
    • Coverings, heat kernels and spanning trees
    • F. Chung and S.-T. Yau, Coverings, heat kernels and spanning trees. J. Combin. 6:163-183 (1999).
    • (1999) J. Combin , vol.6 , pp. 163-183
    • Chung, F.1    Yau, S.-T.2
  • 36
    • 36149049176 scopus 로고
    • Renormalisation on Sierpinski-type fractals
    • R. Hilfer and A. Blumen, Renormalisation on Sierpinski-type fractals. J. Phys. A: Math. Gen. 17:L537-L545 (1984).
    • (1984) J. Phys. A: Math. Gen , vol.17
    • Hilfer, R.1    Blumen, A.2
  • 37
    • 0242329395 scopus 로고    scopus 로고
    • High-precision entropy values for spanning trees in lattices
    • J. L. Felker and R. Lyons, High-precision entropy values for spanning trees in lattices. J. Phys. A: Math. Gen. 36:8361-8365 (2003).
    • (2003) J. Phys. A: Math. Gen , vol.36 , pp. 8361-8365
    • Felker, J.L.1    Lyons, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.