메뉴 건너뛰기




Volumn 19, Issue 3-4, 2001, Pages 194-246

Random maps, coalescing saddles, singularity analysis, and airy phenomena

Author keywords

Airy function; Analytic combinatorics; Coalescing saddle points; Multiconnectivity; Planar map; Random generation; Random graph; Singularity analysis; Stable law

Indexed keywords


EID: 0035539862     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.10021     Document Type: Article
Times cited : (121)

References (54)
  • 1
    • 0004245694 scopus 로고
    • Dover, New York A reprint of the tenth National Bureau of Standards edition, 1964
    • M. Abramowitz and I.A. Stegun, Handhook of mathematical functions, Dover, New York 1973. [A reprint of the tenth National Bureau of Standards edition, 1964].
    • (1973) Handhook of Mathematical Functions
    • Abramowitz, M.1    Stegun, I.A.2
  • 2
    • 84974625368 scopus 로고
    • "Planar maps and airy phenomena," automata, languages, and programming (2000)
    • E.W.U. Montanari, J. Rolim (Editors), Lecture Notes in Computer Science, Geneva, July
    • C. Banderier, P. Flajolet, G. Schaeffer, and M. Soria, "Planar maps and Airy phenomena," Automata, languages, and programming (2000), E.W.U. Montanari, J. Rolim (Editors), Lecture Notes in Computer Science, 1853, pp. 388-402, Proceedings of the 27th ICALP Conference, Geneva, July 2000.
    • (1853) Proceedings of the 27th Icalp Conference , pp. 388-402
    • Banderier, C.1    Flajolet, P.2    Schaeffer, G.3    Soria, M.4
  • 4
    • 0015896876 scopus 로고
    • Central and local limit theorems applied to asymptotic enumeration
    • E.A. Bender, Central and local limit theorems applied to asymptotic enumeration, J Combin Theory 15 (1973), 91-111.
    • (1973) J Combin Theory , vol.15 , pp. 91-111
    • Bender, E.A.1
  • 5
    • 0016114863 scopus 로고
    • Asymptotic methods in enumeration
    • E.A. Bender, Asymptotic methods in enumeration. SIAM Review 16(4) (1974), 485-515.
    • (1974) SIAM Review , vol.16 , Issue.4 , pp. 485-515
    • Bender, E.A.1
  • 6
    • 0007509181 scopus 로고
    • Some unsolved problems in map enumeration
    • E.A. Bender, Some unsolved problems in map enumeration. Bull Inst Combin Appl 3 (1991), 51-56.
    • (1991) Bull Inst Combin Appl , vol.3 , pp. 51-56
    • Bender, E.A.1
  • 7
    • 84990706258 scopus 로고
    • Largest 4-connected components of 3-connected planar triangulations
    • E.A. Bender, L.B. Richmond, and N.C. Wormald, Largest 4-connected components of 3-connected planar triangulations. Rand Struct Alg 7(4) (1995), 273-285.
    • (1995) Rand Struct Alg , vol.7 , Issue.4 , pp. 273-285
    • Bender, E.A.1    Richmond, L.B.2    Wormald, N.C.3
  • 8
    • 0004276231 scopus 로고
    • Dover, New York, A reprint of the second Holt, Rinehart and Winston edition, 1975
    • N. Bleistein, and R.A Handelsman, Asymptotic Expansions of Integrals. Dover, New York, 1986. [A reprint of the second Holt, Rinehart and Winston edition, 1975].
    • (1986) Asymptotic Expansions of Integrals
    • Bleistein, N.1    Handelsman, R.A.2
  • 9
    • 0001615732 scopus 로고
    • Uniform asymptotic expansion of charlier polynomials
    • R. Bo and R. Wong, Uniform asymptotic expansion of Charlier polynomials, Meth Appl Anal 1(3) (1994), 294-313.
    • (1994) Meth Appl Anal , vol.1 , Issue.3 , pp. 294-313
    • Bo, R.1    Wong, R.2
  • 11
    • 0000268033 scopus 로고    scopus 로고
    • Enumeration of planar constellations
    • M. Bousquet-Mélou and G. Schaeffer, Enumeration of planar constellations, Adv Appl Math 24(4) (2000), 337-368.
    • (2000) Adv Appl Math , vol.24 , Issue.4 , pp. 337-368
    • Bousquet-Mélou, M.1    Schaeffer, G.2
  • 13
    • 0003930163 scopus 로고
    • Dover, New York A reprint of the third North Holland edition, 1970 (first edition, 1958)
    • N.G. De Bruijn, Asymptotic methods in analysis, Dover, New York 1981. [A reprint of the third North Holland edition, 1970 (first edition, 1958)].
    • (1981) Asymptotic Methods in Analysis
    • De Bruijn, N.G.1
  • 14
    • 0000486106 scopus 로고    scopus 로고
    • Images and preimages in random mappings
    • M. Drmota and M. Soria, Images and preimages in random mappings, SIAM J Discrete Math 10(2) (1997), 246-269.
    • (1997) SIAM J Discrete Math , vol.10 , Issue.2 , pp. 246-269
    • Drmota, M.1    Soria, M.2
  • 15
    • 0007551295 scopus 로고    scopus 로고
    • Q-grammars and wall polyominoes
    • P. Duchon, Q-grammars and wall polyominoes, Ann Combin 3 (1999), 311-321.
    • (1999) Ann Combin , vol.3 , pp. 311-321
    • Duchon, P.1
  • 19
    • 0007554179 scopus 로고    scopus 로고
    • Singularity analysis and asymptotics of Bernoulli sums
    • P. Flajolet, Singularity analysis and asymptotics of Bernoulli sums, Theor Comput Sci 215(1/2) (1999), 371-381.
    • (1999) Theor Comput Sci , vol.215 , Issue.1-2 , pp. 371-381
    • Flajolet, P.1
  • 20
    • 0001107358 scopus 로고
    • The first cycles in an evolving graph
    • P. Flajolet, D.E. Knuth, and B. Pittel, The first cycles in an evolving graph, Discrete Math 75 (1989), 167-215.
    • (1989) Discrete Math , vol.75 , pp. 167-215
    • Flajolet, P.1    Knuth, D.E.2    Pittel, B.3
  • 22
    • 0007469365 scopus 로고    scopus 로고
    • To appear in 16p
    • P. Flajolet and G. Louchard, Analytic variations on the Airy distribution, Technical Report TR-01-15, Alcom-FT Project, 2001. [To appear in Algorithmica, Special Issue on Analysis of Algorithms 2002; 16p].
    • (2002) Algorithmica, Special Issue on Analysis of Algorithms
  • 23
    • 0000640693 scopus 로고
    • Singularity analysis of generating functions
    • P. Flajolet and A.M. Odlyzko, Singularity analysis of generating functions, SIAM J Applied Math 3(2) (1990), 216-240.
    • (1990) SIAM J Applied Math , vol.3 , Issue.2 , pp. 216-240
    • Flajolet, P.1    Odlyzko, A.M.2
  • 24
    • 19544388116 scopus 로고    scopus 로고
    • On the analysis of linear probing hashing
    • P. Flajolet P. Poblete, and A. Viola, On the analysis of linear probing hashing, Algorithmica 22(4) (1998), 490-515.
    • (1998) Algorithmica , vol.22 , Issue.4 , pp. 490-515
    • Flajolet, P.1    Poblete, P.2    Viola, A.3
  • 26
    • 0000202919 scopus 로고
    • General combinatorial schemas: Gaussian limit distributions and exponential tails
    • P. Flajolet and M. Soria, General combinatorial schemas: Gaussian limit distributions and exponential tails, Discrete Math 114 (1993), 159-180.
    • (1993) Discrete Math , vol.114 , pp. 159-180
    • Flajolet, P.1    Soria, M.2
  • 27
    • 0000093146 scopus 로고
    • Uniform asymptotic expansions of Laguerre polynomials
    • C.L. Frenzen and R. Wong, Uniform asymptotic expansions of Laguerre polynomials, SIAM J Math Anal 19(5) (1988), 1232-1248.
    • (1988) SIAM J Math Anal , vol.19 , Issue.5 , pp. 1232-1248
    • Frenzen, C.L.1    Wong, R.2
  • 28
    • 0032661468 scopus 로고    scopus 로고
    • The size of the largest components in random planar maps
    • electronic
    • Z. Gao and N.C. Wormald, The size of the largest components in random planar maps, SIAM J Discrete Math 12(2) (1999), 217-228 (electronic).
    • (1999) SIAM J Discrete Math , vol.12 , Issue.2 , pp. 217-228
    • Gao, Z.1    Wormald, N.C.2
  • 29
    • 0007468685 scopus 로고
    • Some results on the asymptotic behaviour of coefficients of large powers of functions
    • D. Gardy, Some results on the asymptotic behaviour of coefficients of large powers of functions, Discrete Math 139(1-3) (1995), 189-217.
    • (1995) Discrete Math , vol.139 , Issue.1-3 , pp. 189-217
    • Gardy, D.1
  • 34
    • 19544364512 scopus 로고    scopus 로고
    • Linear probing and graphs
    • D.F. Knuth, Linear probing and graphs, Algorithmica 22(4) (1998), 561-568.
    • (1998) Algorithmica , vol.22 , Issue.4 , pp. 561-568
    • Knuth, D.F.1
  • 36
    • 0001292619 scopus 로고    scopus 로고
    • A pattern of asymptotic vertex valency distributions in planar maps
    • V.A. Liskovets, A pattern of asymptotic vertex valency distributions in planar maps, J Combin Theory Ser B 75(1) (1999), 116-133.
    • (1999) J Combin Theory Ser B , vol.75 , Issue.1 , pp. 116-133
    • Liskovets, V.A.1
  • 37
    • 0021625402 scopus 로고
    • The Brownian excursion: A numerical analysis
    • G. Louchard, The Brownian excursion: a numerical analysis, Comput Math Appl 10(6) (1984), 413-417.
    • (1984) Comput Math Appl , vol.10 , Issue.6 , pp. 413-417
    • Louchard, G.1
  • 38
    • 0001270611 scopus 로고
    • On the altitude of nodes in random trees
    • A. Meir, and J.W. Moon, On the altitude of nodes in random trees, Can J Math 30 (1978), 997-1015.
    • (1978) Can J Math , vol.30 , pp. 997-1015
    • Meir, A.1    Moon, J.W.2
  • 39
    • 0000278117 scopus 로고
    • Asymptotic enumeration methods
    • R. Graham, M. Grötschel, and L. Lovász, (Editors), Elsevier, Amsterdam
    • A.M. Odlyzko, "Asymptotic enumeration methods," Handbook of combinatorics, vol. II, R. Graham, M. Grötschel, and L. Lovász, (Editors), Elsevier, Amsterdam, 1995, pp. 1063-1229.
    • (1995) Handbook of Combinatorics , vol.2 , pp. 1063-1229
    • Odlyzko, A.M.1
  • 42
    • 36149033043 scopus 로고
    • Uniform q-series asymptotics for staircase polygons
    • T. Prellberg, Uniform q-series asymptotics for staircase polygons, J Phys A: Math Gen 28 (1995), 1289-1304.
    • (1995) J Phys A: Math Gen , vol.28 , pp. 1289-1304
    • Prellberg, T.1
  • 47
    • 0007508170 scopus 로고    scopus 로고
    • Enumerating graphs and brownian motion
    • J. Spencer, Enumerating graphs and Brownian motion, Commun Pure Appl Math 50 (1997), 293-296.
    • (1997) Commun Pure Appl Math , vol.50 , pp. 293-296
    • Spencer, J.1
  • 48
    • 0000703623 scopus 로고
    • A Bernoulli excursion and its various applications
    • L. Takacs, A Bernoulli excursion and its various applications, Adv Appl Probab 23 (1991), 557-585.
    • (1991) Adv Appl Probab , vol.23 , pp. 557-585
    • Takacs, L.1
  • 49
    • 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
  • 50
    • 17644365706 scopus 로고
    • Planar enumeration
    • Cambridge, Academic Press, London
    • W.T. Tutte, "Planar enumeration," Graph theory and combinatorics (Cambridge, 1983), Academic Press, London, 1984, pp. 315-319.
    • (1983) Graph Theory and Combinatorics , pp. 315-319
    • Tutte, W.T.1
  • 54
    • 0003358330 scopus 로고
    • One-dimensional stable distributions
    • Providence, RI, Translated from the Russian by H.H. McFaden, Translation edited by Ben Silver
    • V.M. Zolotarev, One-dimensional stable distributions, American Mathematical Society, Providence, RI, 1986. [Translated from the Russian by H.H. McFaden, Translation edited by Ben Silver.]
    • (1986) American Mathematical Society
    • Zolotarev, V.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.