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Some other home pages of people who do combinatorial asymptotics.

  • 118. (with E.R. Canfield and Z.C. Gao) Locally restricted compositions IV. Nearly free large parts and gap-freeness. Electron. J. Combin. 19(4) (2012) P14 29pp. pdf
  • 117. (with Z.C. Gao) Asymptotic enumeration of labelled graphs by genus. Electron. J. Combin. 18(1) (2011) P13 28pp.  pdf
  • 116. (with E.R. Canfield) Locally restricted compositions III. Adjacent-part periodic inequalities. Electron. J. Combin. 17(1) (2010) R145 9pp.  pdf
  • 115. (with A.B. Olde Daalhuis, Z.C. Gao, L.B. Richmond and N. Wormald) Asymptotics of Some Convolutional Recurrences. Electron. J. Combin. 17(1) (2010) R1 11pp.  pdf
  • 114. (with E.R. Canfield) Locally restricted compositions II. General restrictions and infinite matrices. Electron. J. Combin. 16(1) (2009) R108 36pp.  pdf   (erratum for p.31 at end)
  • 113. (with Z.C. Gao and L.B. Richmond) The map asymptotics constant tg. Electron. J. Combin. 15 (2008) R51 8pp.  pdf  (corrected version)
  • 112. (with E.R. Canfield and L.B. Richmond) Coefficients of functional composition often grow smoothly. Electron. J. Combin. 15 (2008) R21 9pp.  pdf
  • 111. (with E.R. Canfield) Locally restricted compositions I. Restricted adjacent differences. Electron. J. Combin. 12 (2005) R57 27pp.  pdf
  • 110. (with G.F. Lawler, R. Pemantle, and H.S. Wilf) Irreducible compositions and the first return to the origin of a random walk.  Sem. Lothar. Comb. 50 (2004) B50h  pdf
  • 109. (with A. Mashatan, D. Panario, and L.B. Richmond) Asymptotics of combinatorial structures with large smallest component. J. Combin. Theory Ser. A 107 (2004) 117-125.  pdf
  • 108. (with W.J. Helton and L.B. Richmond) Asymptotics of permutations with specified rises and falls. Electron. J. Combin. 10 (2003) R40 27pp.  pdf
  • 107. (with E.R. Canfield, L.B. Richmond, and H.S. Wilf) A discontinuity in the distribution of fixed point sums. Electron. J. Combin. 10 (2003) R15 18pp.  pdf
  • 106. (with Z.C. Gao and N.C. Wormald) The number of labeled 2-connected planar graphs. Electron. J. Combin. 9 (2002) R43 13pp.  pdf
  • 105. (with J. Bell, P.J. Cameron, and L.B. Richmond) Asymptotics for the probability of connectedness and the distribution of number of components. Electron. J. Combin. 7 (2000) R33 22pp.  pdf
  • 104. (with E.R. Canfield) Intersections of randomly embedded sparse graphs are Poisson. Electron. J. Combin. 6 (1999) R36 10pp.  pdf
  • 103. (with P.J. Cameron, A.M. Odlyzko, and L.B. Richmond) Connectedness, classes and cycle index. Combin. Probab. and Comput. 8 (1999) 31-43.
  • 102. (with E.R. Canfield) An approximate probabilistic model for structured Gaussian elimination. J. Algorithms 31 (1999) 271-290.
  • 101. (with K.J. Compton and L.B. Richmond) 0-1 laws for maps. Random Structures and Algorithms  14 (1999) 215-237. pdf
  • 100. (with L.B. Richmond) Multivariate asymptotics for products of large powers with application to Lagrange inversion. Electron. J. Combin. 6 (1999) R8 21pp.  pdf
  • 99. (with L.B. Richmond) A multivariate Lagrange inversion formula for asymptotic calculations. Electron. J. Combin. 5 (1998) R33 4pp.  pdf
  • 98. (with G. Williamson) Periodic sorting using minimum delay, recursively constructed merging networks. Electron. J. Combin. 5 (1998) R5 21pp.  pdf
  • 97. (with E.R. Canfield and B.D. McKay) The asymptotic number of labeled graphs with n vertices, q edges, and no isolated vertices. J. Combin. Theory Ser. A 80 (1997) 124-150.  pdf
  • 96. (with E.R. Canfield, Z.C. Gao, and L.B. Richmond) Submap density and asymmetry results for two parameter map families. Combin. Probab. and Comput. 6 (1997) 17-25.  pdf
  • 95. (with E.R. Canfield) The fraction of subspaces of GF(q)^n with a specified number of minimal weight vectors is asymptotically Poisson. Electron. J. Combin. 4 (1997) R3 8pp.  pdf
  • 94. (with L.B. Richmond) Admissible functions and asymptotics for labeled structures by number of components. Electron. J. Combin. 3 (1996) R34 23pp.  pdf
  • 93. (with E.R. Canfield) Log-concavity and related properties of the cycle index polynomials. J. Combin. Theory Ser. A 74 (1996) 57-70.  pdf
  • 92. (with Z.C. Gao, L.B. Richmond, and N.C. Wormald) Asymptotic properties of rooted 3-connected maps on surfaces. J. Austral. Math. Soc. 60 (1996) 31-41.
  • 91. (with L.B. Richmond and N. Wormald) Largest 4-connected components of 3-connected planar triangulations. Random Structures and Algorithms 7 (1995) 273-285.
  • 90. (with Z.C. Gao, L.B. Richmond, and N.C. Wormald) Almost all rooted maps have large representativity. J. Graph Theory 18 (1994) 545-555.  pdf
  • 89. (with O. Patashnik and H. Rumsey, Jr.) Pizza slicing, phi's, and the Riemann hypothesis. Amer. Math. Monthly 101 (1994) 307-317.
  • 88. (with E.R. Canfield) The number of degree restricted rooted maps on the sphere. SIAM J. Discrete Math. 7 (1994) 9-15.  pdf
  • 87. (with L.B. Richmond and N.C. Wormald) Submaps of maps IV: Degree restricted nonplanar maps. Ars Combinatoria 35A (1993) 135-142.
  • 86. (with F. Kochman) The distribution of subword counts is usually normal. European J. Combin. 14 (1993) 265-275.
  • 85. (with E.R. Canfield and L.B. Richmond) The asymptotic number of rooted maps on a surface II: Enumeration by vertices and edges. J. Combin. Theory Ser. A 63 (1993) 318-329.
  • 84. (with E.R. Canfield) Enumeration of degree restricted maps on the sphere. DIMACS Series in Discrete Math. and Theoret. Computer Science, 9 (1993) 13-16. (An extended abstract of 88.)
  • 83. (with E.R. Canfield and B.D McKay) The asymptotic number of labelled weakly-connected digraphs with a given number of vertices and edges. Australasian J. Combin. 6 (1992) 119-124.
  • 82. (with E.R. Canfield and B.D. McKay) Asymptotic properties of labeled connected graphs. Random Structures and Algorithms 3 (1992) 183-202.  pdf
  • 81. (with L.B. Richmond) Submaps of maps III: k-connected nonplanar maps. J. Combin. Theory Ser. B 55 (1992)
    125-132.
  • 80. (with Z.C. Gao, W.D. McCuaig, and L.B. Richmond) Submaps of maps II: Cyclically $k$-connected planar cubic maps. J. Combin. Theory Ser. B 55 (1992) 118-124.
  • 79. (with Z.C. Gao and L.B. Richmond) Submaps of maps I: General 0-1 laws. J. Combin. Theory Ser. B 55 (1992) 104-117.
  • 78. (with H. Rumsey, Jr.) Consider perl. Notices Amer. Math. Soc. 39 (1992) 187-189.
  • 77. (with R. Coley, D.P. Robbins, and H. Rumsey, Jr.) Enumeration of subspaces by dimension sequence. J. Combin. Theory Ser. A 59 (1992) 1-11.
  • 76. Some unsolved problems in map enumeration. Bull. Inst. Combin. and Its Appl. 3 (1991) 51-56.  pdf
    I update the status of the problems, so the file here has addenda.  Last updated Oct. 2002.
  • 75. (with E.R. Canfield) The number of rooted maps on an orientable surface. J. Combin. Theory Ser. B 53 (1991) 293-299.
  • 74. (with L.B. Richmond) 3-connected embeddings have few singular edges. J. Graph Theory 14 (1990) 475-477.
  • 73. (with E.R. Canfield and B.D. McKay) The asymptotic number of labeled connected graphs with a given number of vertices and edges. Random Structures and Algorithms 1 (1990) 127-169.
  • 72. (with F. Kochman and D.B. West) Adding up powers (classroom note). Amer. Math. Monthly 97 (1990) 139-143.
  • 71. (with J.T. Butler) On the size of PLA's required to realize binary and multiple-valued functions. IEEE Trans. Comput. 38 (1989) 82-98.
  • 70. (with E.R. Canfield) Face sizes of 3-polytopes. J. Combin. Theory Ser. B 46 (1989) 58-65.
  • 69. (with N.C. Wormald) The asymptotic number of rooted nonseparable maps on a surface. J. Combin. Theory Ser. B 49 (1998) 370-380.
  • 68. (with E.R. Canfield and R.W. Robinson) The enumeration of maps on the torus and the projective plane. Canad. Math. Bull. 31 (1988) 257-271.
  • 67. (with R.W. Robinson) The asymptotic number of acyclic digraphs II. J. Combin. Theory Ser. B 44 (1988) 363-369.
  • 66. (with E.R. Canfield and R.W. Robinson) The asymptotic number of tree-rooted maps on a surface. J. Combin. Theory Ser A 48 (1988) 156-164.
  • 65. (with N.C. Wormald) The number of rooted convex polyhedra. Canad. Math. Bull. 31 (1988) 99-102.
  • 64. (with N.C. Wormald) Random trees in random graphs. Proc. Amer. Math. Soc. 103 (1988) 314-320.
  • 63. (with C. Praeger and N.C. Wormald) Optimal worst case trees. Acta Informatica 24 (1987) 475-489.
  • 62. The number of three-dimensional convex polyhedra. Amer. Math. Monthly 94 (1987) 7-21.
  • 61. (with E.R. Canfield) The asymptotic number of rooted maps on a surface. J. Combin. Theory Ser. A 43 (1986) 244-257.
  • 60. (with L.B. Richmond) A survey of the asymptotic behaviour of maps. J. Combin. Theory Ser. B 40 (1986) 297-329.
  • 59. (with L.B. Richmond, R.W. Robinson and N.C. Wormald) The asymptotic number of acyclic digraphs I. Combinatorica 6 (1986) 15-22.
  • 58. (with L.B. Richmond) A generalisation of Canfield's formula. J. Combin. Theory Ser. A 41 (1986) 50-60.
  • 57. (with N.C. Wormald) Almost all convex polyhedra are asymmetric. Canad. J. Math. 37 (1985) 854-871.
  • 56. (with L.B. Richmond) Asymptotic enumeration of labelled multigraphs by vertices, edges and degree parities. J. Graph Theory 10 (1986) 41-46.
  • 55. (with H.S. Wilf) A theoretical analysis of backtracking in the graph coloring problem. J. Algorithms 6 (1985) 275-282.
  • 54. (with J.T. Butler) Enumeration of structured flowcharts. J. Assoc. Comput. Mach. 32 (1985) 537-542.
  • 53. (with A.M. Odlyzko and L.B. Richmond) The asymptotic number of irreducible partitions. European. J. Combin. 6 (1985) 1-6.
  • 52. (with J.T. Butler and H.G. Kerkhoff) Comparing the SUM with the MAX for use in four-valued PLA's. Proc. 15th Intl. Symp. Multi-valued Logic (1985) 30-35.
  • 51. (with N.C. Wormald) The number of loopless planar maps. Discrete Math. 54 (1985) 235-237.  This result appeared earlier:
    T.R.S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps.  J. Combin. Theory Ser. B 38 (1985).
  • 50. (with D. Zeilberger) Some asymptotic bijections. J. Combin. Theory Ser. A 18 (1975) 222-259.
  • 49. (with L.B. Richmond) The asymptotic enumeration of rooted convex polyhedra. J. Combin. Theory Ser. B 36 (1984) 276-283.
  • 48. (with L.B. Richmond and N.C. Wormald) Almost all chordal graphs split. J. Austral. Math. Soc. Ser. A 38 (1985) 214-221.
  • 47. (with J.S. Devitt and L.B. Richmond) Partitions of multisets II. Discrete Math. 50 (1984) 1-8.
  • 46. (with L.B. Richmond) An asymptotic expansion for the coefficients of some formal power series II: Lagrange inversion. Discrete Math. 50 (1984) 135-142.
  • 45. (with G. Viennot and S.G. Williamson) Global analysis of the delete-contract recursion for graphs and matroids. Linear and Multilinear Algebra 15 (1984) 133-160.
  • 44. (with T.J. Case and M.E. Gilpin) Perturbation experiments in community ecology. Ecology 65 (1984) 1-13.
  • 43. (with L.B. Richmond) Correlated random walks. Ann. Probability 12 (1984) 274-278.
  • 42. (with L.B. Richmond and S.G. Williamson) Central and local limit theorems applied to asymptotic enumeration III: Matrix recursions. J. Combin. Theory Ser. A 35 (1983) 263-278.
  • 41. (with E. R. Canfield) Enumeration of connected invariant graphs. J. Combin. Theory Ser. B 34 (1983) 268-278.
  • 40. (with L.B. Richmond) Central and local limit theorems applied to asymptotic enumeration II: Multivariate generating functions. J. Combin. Theory Ser. A 34 (1983) 255-265.
  • 39. (with J. Arney) Random mappings with constraints on coalescence and the number of origins. Pacific J. Math. 103 (1982) 269-294.
  • 38. (with T.J. Case and M.E. Gilpin) Counter-intuitive oscillations in systems of competition and mutualism. Amer. Naturalist 119 (1982) 584-588.
  • 37. (with T.J. Case) Testing for higher order interactions. Amer. Naturalist 118 (1981) 920-929.
  • 36. (with T.J. Case) Is recombination advantageous in fluctuating spatially heterogeneous environments? J. Theoret. Biol. 90 (1981) 181-190.
  • 35. (with E.R. Canfield) Fanout-free functions (unsolved problem). Amer. Math. Monthly. 88 (1981) 278-280.
  • 34. (with J.T. Butler) Enumeration of functions realized by fanout-free networks of general multi-valued gates. Proc. Ninth Intl. Symp. on Multi-valued Logic (Bath, 1979) 94-103.
  • 33. A recurrent problem (letter to the editor). Computing Surveys 11 (1979) 67-68.
  • 32. The number of fanout-free functions with various gates. J. Assoc. Comput. Mach. 27 (1980) 181-190.
  • 31. A driving hazard revisited (classroom note). SIAM Rev. 21 (1979) 136-138.
  • 30. (with J.T. Butler) Asymptotic approximation for the number of fanout-free functions. IEEE Trans. Comput. 27 (1978) 1180-1183.
  • 29. (with E.R. Canfield) The asymptotic number of labeled graphs with given degree sequences. J. Combin. Theory Ser. A 24 (1978) 296-307.
  • 28. (with J.R. Goldman) On the applications of Mobius inversion in combinatorial analysis. Amer. Math. Monthly 82 (1975) 789-803.
  • 27. (with N.P. Herzberg) Some diophantine equations related to the quadratic form ax^2+by^2. Advances in Mapt. Supp. Studies 6. Studies in Algebra and Number Theory (1979) 219-272.
  • 26. (with N.P. Herzberg) Some diophantine equations related to the quadratic form ax^2+by^2 (summary). Bull. Amer. Math. Soc. 81 (1975) 161-162.
  • 25. (with J.V. Brawley) Similarity to symmetric matrices over field which are not formally real. Linear and Multilinear Algebra 3 (1975) 3-8.
  • 24. The asymptotic number of non-negative matrices with given row and column sums. Discrete Math. 10 (1974) 217-223.
  • 23. An asymptotic expansion for the coefficients of some formal power series. J. London Math. Soc. 9 (1975) 451-458.
  • 22. Asymptotic methods in enumeration. SIAM Rev. 16 (1974).
          Comments and errata:
    • For a more up to date and much more extensive survey, see A.M. Odlyzko's chapter in Handbook of Combinatorics, Elsevier (1995) vol. II 1063-1229.
    • Theorem 2 appeared Problem 178 in Part I of Volume 1 of Polya and Szego's Problems and Theorems in Analysis.
    • The hypotheses of Theorem 5 are inadequate.  For a correct theorem, see A. Meir and J.W. Moon, On an asymptotic method in enumeration, J. Combin. Theory Ser. A  51 (1989) 77-89.
    • SIAM Rev. 18 (1976) 292 contains minor errata.
  • 21. (with N.P. Herzberg) Characteristic polynomials of symmetric matrices III: Some counterexamples. Linear and Multilinear Algebra 2 (1974) 173-178.
  • 20. Characteristic polynomials of symmetric matrices II: Local number fields. Linear and Multilinear Algebra 2 (1974) 55-63.
  • 19. On Buckhiester's enumeration of n x n matrices. J. Combin. Theory Ser. A 17 (1974) 273-274.
  • 18. Partitions of multisets. Discrete Math. 9 (1974) 301-311.
  • 17. Convex n-ominoes. Discrete Math. 8 (1974) 219-226.  The value of f in (11) is incorrect.  The correct value, f=2.67564, is in the abstract.
  • 16. A lifting formula for formal power series. Proc. Amer. Math. Soc. 42 (1974) 301-311.
  • 15. A lifting formula for the Hilbert symbol. Proc. Amer. Math. Soc. 40 (1973) 63-65.  Would be better called a going down formula.
  • 14. Central and local limit theorems applied to asymptotic enumeration. J. Combin. Theory Ser. A 15 (1973) 91-111.
  • 13. (with N.P. Herzberg) Symmetric matrices, characteristic polynomials, and Hilbert symbols over local fields (summary). Bull. Amer. Math. Soc. 79 (1973) 518-520.
  • 12. (with L.P. Neuwirth) Traffic flow: Laplace transforms (classroom note). Amer. Math. Monthly 80 (1973) 417-423.
  • 11. Teaching applicable mathematics (classroom note). Amer. Math. Monthly 80 (1973) 302-307.
  • 10. (with D.E. Knuth) Enumeration of plane partitions. J. Combin. Theory Ser. A 13 (1972) 40-54.
  • 9. A generalized q-binomial Vandermonde convolution. Discrete Math. 1 (1971) 115-119.
  • 8. (with J.R. Goldman) Enumerative uses of generating functions. Indiana Univ. Math. J. 20 (1971) 753-765.
  • 7. The dimensions of matrices with a given minimal polynomial. Linear Alg. and Appl. 3 (1970) 115-123.
  • 6. (with T.W. Tucker) The exponents of strongly connected graphs. Canad. J. Math. 21 (1969) 769-782.
  • 5. Characteristic polynomials of symmetric matrices. Pacific J. Math. 25 (1968) 433-441.
  • 4. Classes of matrices and quadratic fields. Linear Alg. and Appl. 3 (1970) 195-201.
  • 3. Classes of matrices over an integral domain. Illinois J. Math. 11 (1967) 697-702.
  • 2. Numerical identities in lattices with an application to Dirichlet products. Proc. Amer. Math. Soc. 15 (1964) 8-13.
  • 1. Area-perimeter relations for two-dimensional lattices. Amer. Math. Monthly 69 (1962) 742-744.