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Volumn 13, Issue 4, 2004, Pages 483-493

On the asymptotic number of plane curves and alternating knots

Author keywords

Asymptotic enumeration; Planar maps; Plane curves

Indexed keywords


EID: 14944356215     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2004.10504557     Document Type: Article
Times cited : (18)

References (28)
  • 1
    • 4244169180 scopus 로고
    • Geometry of a Two-Dimensional Quantum Gravity: Numerical Study
    • M. E. Agishtein and A.A. Migdal. “Geometry of a Two-Dimensional Quantum Gravity: Numerical Study.” Nucl. Phys. B 350 (1991), 690-728.
    • (1991) Nucl. Phys. B , vol.350 , pp. 690-728
    • Agishtein, M.E.1    Migdal, A.A.2
  • 4
    • 0000567226 scopus 로고
    • Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge
    • F. David. “Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge.” Mod. Phys. Lett. A 3 (1988), 1651-1656.
    • (1988) Mod. Phys. Lett. A , vol.3 , pp. 1651-1656
    • David, F.1
  • 5
    • 33646060263 scopus 로고
    • Conformal Field Theory and 2D Quantum Gravity
    • J. Distler and H. Kawai. “Conformal Field Theory and 2D Quantum Gravity.” Nucl. Phys. B 321 (1989), 509-527.
    • (1989) Nucl. Phys. B , vol.321 , pp. 509-527
    • Distler, J.1    Kawai, H.2
  • 7
    • 38248998905 scopus 로고
    • A Pattern in the Asymptotic Number of Rooted Maps on Surfaces
    • Z. Gao. “A Pattern in the Asymptotic Number of Rooted Maps on Surfaces.” J. Combin. Theory Ser. A 64 (1993), 246-264.
    • (1993) J. Combin. Theory Ser. A , vol.64 , pp. 246-264
    • Gao, Z.1
  • 8
    • 0005273942 scopus 로고    scopus 로고
    • On the Number of Topological Types of Plane Curves
    • (English translation in, Russian Math. Surveys 53 (1998), 626-627
    • S. M. Gusein-Zade and F. S. S. Duzhin. “On the Number of Topological Types of Plane Curves.” Uspekhi Math. Nauk. 53 (1998), 197-198. English translation in Russian Math. Surveys 53 (1998), 626-627.
    • (1998) Uspekhi Math. Nauk , vol.53 , pp. 197-198
    • Gusein-Zade, S.M.1    Duzhin, F.S.S.2
  • 9
    • 0037424189 scopus 로고    scopus 로고
    • Dense Loops, Supersymmetry, and Goldstone Phases in Two Dimensions
    • arXiv:cond-mat/0205033
    • J. L. Jacobsen, N. Read, and H. Saleur. “Dense Loops, Supersymmetry, and Goldstone Phases in Two Dimensions.” Phys. Rev. Lett. 90 (2003), arXiv:cond-mat/0205033.
    • (2003) Phys. Rev. Lett , vol.90
    • Jacobsen, J.L.1    Read, N.2    Saleur, H.3
  • 10
    • 0036672543 scopus 로고    scopus 로고
    • A Transfer Matrix Approach to the Enumeration of Knots
    • arXiv:math-ph/0102015
    • J. L. Jacobsen and P. Zinn-Justin, “A Transfer Matrix Approach to the Enumeration of Knots.” J. Knot Theor. Ramif. 11 (2002), 739-758. arXiv:math-ph/0102015.
    • (2002) J. Knot Theor. Ramif , vol.11 , pp. 739
    • Jacobsen, J.L.1    Zinn-Justin, P.2
  • 11
    • 0035729196 scopus 로고    scopus 로고
    • A Transfer Matrix Approach to the Enumeration of Colored Links
    • arXiv:math-ph/0104009
    • J. L. Jacobsen and P. Zinn- Justin. “A Transfer Matrix Approach to the Enumeration of Colored Links.” J. Knot Theor. Ramif. 10 (2001), 1233-1267. arXiv:math-ph/0104009.
    • (2001) J. Knot Theor. Ramif , vol.10 , pp. 1233-1267
    • Jacobsen, J.L.1    Zinn-Justin, P.2
  • 12
    • 0000533445 scopus 로고
    • Critical Properties of Randomly Triangulated Planar Random Surfaces
    • V. A. Kazakov, A. A. Migdal, and I. K. Kostov. “Critical Properties of Randomly Triangulated Planar Random Surfaces.” Phys.Lett. B 157 (1985), 295-300.
    • (1985) Phys.Lett. B , vol.157 , pp. 295
    • Kazakov, V.A.1    Migdal, A.A.2    Kostov, I.K.3
  • 15
    • 0031599142 scopus 로고    scopus 로고
    • Mersenne Twister: A 623-Dimensionally Equidistributed Pseudo-Random Number Generator
    • M. Matsumoto and T. Nishimura. “Mersenne Twister: A 623-Dimensionally Equidistributed Pseudo-Random Number Generator.” ACM TYansactions on Modeling and Computer Simulation 8:1 (1998), 3-30.
    • (1998) ACM Tyansactions on Modeling and Computer Simulation , vol.8 , Issue.1 , pp. 3-30
    • Matsumoto, M.1    Nishimura, T.2
  • 16
    • 0000442326 scopus 로고
    • Exact Critical Point and Exponents of the O(N) Model in Two Dimensions
    • B. Nienhuis. “Exact Critical Point and Exponents of the O(n) Model in Two Dimensions.” Phys. Rev. Lett. 49 (1982), 1062-1065.
    • (1982) Phys. Rev. Lett. , vol.49 , pp. 1062-1065
    • Nienhuis, B.1
  • 17
    • 0001636042 scopus 로고    scopus 로고
    • Exact Spectra of Conformal Supersymmetric Nonlinear Sigma Models in Two Dimensions
    • arXiv:hep-th/0106124
    • N. Read and H. Saleur. “Exact Spectra of Conformal Supersymmetric Nonlinear Sigma Models in Two Dimensions.” Nucl. Phys. B 613 (2001), 409-444. arXiv:hep-th/0106124.
    • (2001) Nucl. Phys. B , vol.613 , pp. 409-444
    • Read, N.1    Saleur, H.2
  • 19
    • 0033164002 scopus 로고    scopus 로고
    • A New Proof of the Gauss Interlace Conjecture
    • P. Rosenstiehl. “A New Proof of the Gauss Interlace Conjecture.” Adv. in Appl. Math. 23:1 (1999), 3-13.
    • (1999) Adv. In Appl. Math , vol.23 , Issue.1 , pp. 3-13
    • Rosenstiehl, P.1
  • 20
    • 13744253226 scopus 로고    scopus 로고
    • Bijective Census and Random Generation of Eulerian Planar Maps with Prescribed Vertex Degrees
    • Research Paper 20, (electronic)
    • G. Schaeffer. “Bijective Census and Random Generation of Eulerian Planar Maps with Prescribed Vertex Degrees.” Electron. J. Combin. 4:1 (1997), Research Paper 20, 14 pp. (electronic).
    • (1997) Electron. J. Combin , vol.4 , Issue.1 , pp. 14
    • Schaeffer, G.1
  • 21
    • 0032628274 scopus 로고    scopus 로고
    • Random Sampling of Large Planar Maps and Convex Polyhedra
    • (electronic). New York: ACM Press
    • G. Schaeffer. “Random Sampling of Large Planar Maps and Convex Polyhedra.” In Annual ACM Symposium on Theory of Computing, pp. 760-769 (electronic). New York: ACM Press, 1999.
    • (1999) Annual ACM Symposium on Theory of Computing , pp. 760-769
    • Schaeffer, G.1
  • 22
    • 0000693589 scopus 로고
    • A Census of Planar Maps
    • W. T. Tutte. “A Census of Planar Maps.” Can. J. Math. 15 (1963), 249-271.
    • (1963) Can. J. Math. , vol.15 , pp. 249-271
    • Tutte, W.T.1
  • 24
    • 0041412566 scopus 로고
    • Combinatorial Algorithms: An Update
    • Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM
    • H. S. Wilf. Combinatorial Algorithms: An Update, Conference Series in Applied Mathematics, 55. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 1989.
    • (1989) Conference Series in Applied Mathematics , vol.55
    • Wilf, H.S.1
  • 26
    • 0038565887 scopus 로고    scopus 로고
    • On the Counting of Colored Tangles
    • arXiv:math-ph/0002020
    • P. Zinn-Justin and J. -B. Zuber. “On the Counting of Colored Tangles.” J. Knot Theor. Ramif. 9 (2000) 1127-1141. arXiv:math-ph/0002020.
    • (2000) J. Knot Theor. Ramif , vol.9 , pp. 1127-1141
    • Zinn-Justin, P.1    Zuber, J.-B.2
  • 27
    • 85083150277 scopus 로고    scopus 로고
    • Random Matrix Models and their Applications
    • MSRI Publications, edited by P. Ble- her and A. Its. Cambridge, UK: Cambridge University Press, arXiv:math-ph/9910010
    • P. Zinn-Justin. “Random Matrix Models and their Applications.” In Proceedings of the 1999 Semester of the MSRI “Random Matrices and their Applications,” MSRI Publications Vol. 40, edited by P. Ble- her and A. Its. Cambridge, UK: Cambridge University Press, 2001. arXiv:math-ph/9910010.
    • (2001) Proceedings of the 1999 Semester of the MSRI , vol.40
    • Zinn-Justin, P.1
  • 28
    • 0037660887 scopus 로고    scopus 로고
    • The General 0(N) Quartic Matrix Model and Its Application to Counting Tangles and Links
    • arXiv:math-ph/0106005
    • P. Zinn-Justin. “The General 0(n) Quartic Matrix Model and Its Application to Counting Tangles and Links.” Commun. Math. Phys. 238 (2003), 287-304. arXiv:math-ph/0106005.
    • (2003) Commun. Math. Phys , vol.238 , pp. 287-304
    • Zinn-Justin, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.