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References

  • 1
    M. J. Ablowitz, A. Ramani, and H. Segur, A connection between nonlinear evolution equations and ordinary differential equations of P-type. I, J Math Phys 21 (1980), 715721.
  • 2
    R. Baeza-Yates, R. Casas, J. Díaz, and C. Martínez, On the average size of the intersection of binary trees, SIAM J Comput 21 (1992), 2432.
  • 3
    M. Barnsley and H. Cornille, General solution of a Boltzmann equation, and the formation of Maxwellian tails, Proc Roy Soc Lond Ser A, Math Phys Sci 374 (1981), 371400.
  • 4
    E. A. Bender, Z. Gao, and L. B. Richmond, The map asymptotics constant inline image, Electron J Combin 15 (2008), 8; Research paper 51.
  • 5
    E. A. Bender, Olde Daalhuis A. B., Z. Gao, L. B. Richmond, and N. Wormald, Asymptotics of some convolutional recurrences, Electron J Combin 17 (2010), 11; Research paper 1.
  • 6
    N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular variation, Cambridge University Press, London, 1987.
  • 7
    M. Bóna, and P. Flajolet, Isomorphism and symmetries in random phylogenetic trees, J Appl Probab 46 (2009), 10051019.
  • 8
    N. Broutin, R. Neininger, and H. Sulzbach, Partial match queries in random quadtrees, In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), Kyoto, Japan, 2012, pp. 10561065; also as Arxiv 1107.2231v1.
  • 9
    D. Bryant, A. McKenzie, and M. Steel, The size of a maximum agreement subtree for random binary trees, In Bioconsensus (Piscataway, NJ, 2000/2001), 2003, pp. 5565; DIMACS Ser. 61, AMS, Providence, RI.
  • 10
    H.-H. Chern and H.-K. Hwang, Partial match queries in random quadtrees, SIAM J Comput 32 (2003), 904915.
  • 11
    R. Conte and M. Musette, The Painlevé handbook, Springer Verlag, Springer, Dordrecht, The Netherlands, 2008.
  • 12
    R. Cooper, A class of recurrence formulae, J London Math Soc 22 (1947), 3140.
  • 13
    A. R. Chowdhury and B. Raton, Painlevé analysis and its applications, Chapman & Hall/CRC, Boca Raton, FL, USA, 2000.
  • 14
    N. Curien and A. Joseph, Partial match queries in two-dimensional quadtrees: A probabilistic approach, Adv Appl Probab 43 (2011), 178194.
  • 15
    A. Delshams and A. Mir, Psi-series of quadratic vector fields on the plane, Publ Mat 41 (1997), 101125.
  • 16
    A. Duch, V. Estivill-Castro, and C. Martínez, Randomized K-dimensional binary search trees, In “Algorithms and Computation (Taejon, 1998),” Springer, Berlin, 1998, pp. 199208; LNCS, 1533.
  • 17
    A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions. Vol. III, McGraw-Hill Book Company, New York-Toronto-London, 955.
  • 18
    M.-I. Fernández-Camacho and J.-R. Sánchez-Couso, Binary search trees, recurrent properties and wave equations, Fund Inform 81 (2007), 409439.
  • 19
    P. Flajolet, G. Gonnet, C. Puech, and J. M. Robson, Analytic variations on quadtrees, Algorithmica 10 (1993), 473500.
  • 20
    P. Flajolet, X. Gourdon, and C. Martínez, Patterns in random binary search trees, Random Struct Algorithms 11 (1997), 223244.
  • 21
    P. Flajolet and A. Odlyzko, Singularity analysis of generating functions, SIAM J Discr Math 3 (1990), 216240.
  • 22
    P. Flajolet, P. Poblete, and A. Viola, On the analysis of linear probing hashing, Algorithmica 22 (1998), 490515.
  • 23
    P. Flajolet and R. Sedgewick, Analytic combinatorics, Cambridge University Press, Cambridge, 2009.
  • 24
    A. V. Gnedin and Y. Yakubovich, Recursive partition structures, Ann Probab 34 (2006), 22032218.
  • 25
    M. A. Hemmi and S. Melkonian, Convergence of psi-series solutions of nonlinear ordinary differential equations, Canad Appl Math Quart 3 (1995), 4388.
  • 26
    E. Hille, On a class of series expansions in the theory of Emden's equation, Proc R Soc Edinburgh Sect A 71 (1973), 95110.
  • 27
    E. Hille, A note on quadratic systems, Proc R Soc Edinburgh Sect A 72 (1974), 1737.
  • 28
    E. Hille, Ordinary differential equations in the complex domain, Wiley-Interscience, New York, 1976; reprinted by Dover Publications, 1997.
  • 29
    J. Horn, Ueber die Reihenentwickelung der Integrale eines Systems von Differentialgleichungen in der Umgebung gewisser singulärer Stellen, J Reine Angew Math 116 (1896), 265306.
  • 30
    E. L. Ince, Ordinary differential equations, Dover, New York, 1926.
  • 31
    D. J. Kleitman, Proportions of irreducible diagrams, Stud Appl Math 49 (1970), 297299.
  • 32
    D. B. Saakian, The calculation of multifractal properties of directed random walks on hierarchic trees with continuous branching, J Stat Mech (in press).
  • 33
    H. M. Mahmoud, Evolution of random search trees, Wiley, New York, 1992.
  • 34
    C. Martínez, Average-case analysis of equality of binary trees under the BST probability model, 1991.
  • 35
    C. Martínez, Statistics under the BST model, Ph.D. Thesis, Universitat Politècnica de Catalunya, 1992; Available at: www.lsi.upc.es/~conrado/.
  • 36
    C. Martínez, A. Panholzer, and H. Prodinger, Partial match queries in relaxed multidimensional search trees, Algorithmica 29 (2001), 181204.
  • 37
    A. D. Polyanin and V. F. Zaitsev, Handbook of exact solutions for ordinary differential equations, CRC Press, Boca Raton, FL, 1995.
  • 38
    R. Neininger and L. Rüschendorf, Limit laws for partial match queries in quadtrees, Ann Appl Probab 11 (2001), 452469.
  • 39
    J.-R. Sánchez-Couso and M.-I. Fernández-Camacho, Reductions in binary search trees, Theoret Comput Sci 355 (2006), 327353.
  • 40
    P. R. Stein and M. S. Waterman, On some new sequences generalizing the Catalan and Motzkin numbers, Discr Math 26 (1979), 261272.
  • 41
    E. M. Wright, A quadratic recurrence of Faltung type, Math Proc Cambridge Philos Soc 88 (1980), 193197.
  • 42
    E. M. Wright, A quadratic recurrence of Faltung type, Math Proc Cambridge Philos Soc 92 (1982), 379; Corrigendum.