Size distribution of the largest component of a random A-mapping

References

[1] Arratia R., Barbour A. D., Tavare S., Logarithmic Combinatorial Structures: A Probabilistic Approach (2003), European Mathematical Society, EMS Monografs of Mathematics, 2003, 363 pp.10.4171/000Search in Google Scholar

[2] Bender E. A. (1974), “Asymptotic methods in enumeration”, SIAM Rev, 16, 485–515.10.1137/1016082Search in Google Scholar

[3] Goncharov V. L., “On the field of combinatory analysis”, Am. Math. Soc. Transl., 19 (1962), 1–46.10.1090/trans2/019/01Search in Google Scholar

[4] Donnelly P. J., Ewens W. J., Padmadisastra S., “Functionals of random mappings: exact and asymptotic results”, Adv. Appl. Probab, 23:3 (1991), 437–455.10.2307/1427616Search in Google Scholar

[5] Ercolani N. M., Ueltschi D., “Cycle structure of random permutations with cycle weights”, arXiv:1102.4796v1 [math.PR], 2011. [6] Ewens W.J., “The sampling theory of selectively neutral alleles”, Theor. Popul. Biol, 3 (1972), 87–112.10.1002/rsa.20430Search in Google Scholar

[6] Ewens W.J., “The sampling theory of selectively neutral alleles”, Theor. Popul. Biol, 3 (1972), 87–112.10.1016/0040-5809(72)90035-4Search in Google Scholar

[7] Ivchenko, G. I.; Medvedev, Yu. I., “On random permutations”, Trudy po diskretnoi matematike, 5 (2002), 73–92 (in Russian).Search in Google Scholar

[8] Ivchenko G. I., Medvedev Yu. I., “The method of V. L. Goncharov and its development in the analysis of various models of random permutations.”, Theory Probab. Appl., 47:3 (2003), 518–526.10.1137/S0040585X97979895Search in Google Scholar

[9] Ivchenko G. I., Medvedev Yu. I., “Statistics of parametric random permutation model”, Trudy po diskretnoi matematike, 8 (2004), 116–127 (in Russian).Search in Google Scholar

[10] Ivchenko G. I., Medvedev Yu. I., “Random combinatorial objects”, Dokl. Math., 69:3 (2004), 344–347.Search in Google Scholar

[11] Ivchenko G. I., Medvedev Yu. I., “Random permutations: a general parametric model”, Discrete Math. Appl., 16:5 (2006), 471-–478.10.1515/156939206779238391Search in Google Scholar

[12] Ivchenko G. I.;Medvedev, Yu. I., “Random combinatorial objects in a general parametric model”, Trudy po diskretnoi matem-atike, 10 (2007), 73–86 (in Russian).Search in Google Scholar

[13] Katz L., “Probability of indecomposability of a random mapping function”, Ann. Math. Statist, 26:3 (1955), 512–517.10.1214/aoms/1177728496Search in Google Scholar

[14] Kolchin, V. F., Random Mappings, Optimization Software, New York, 1986.Search in Google Scholar

[15] Kolchin V. F., Random Graphs, Cambridge Univ. Press, Cambridge, 1999.10.1017/CBO9780511721342Search in Google Scholar

[16] Pavlov A. I., “On the number of substitutions with cycle lengths from a given set 445–459.”, Discrete Math. Appl., 2 (1992), 445–459.10.1515/dma.1992.2.4.445Search in Google Scholar

[17] Pavlov Yu .L., Random forests, VSP, Utrecht, 2000, 122 pp.10.1515/9783110941975Search in Google Scholar

[18] Sachkov V. N., “Mappings of a finite set with limitations on contours and height”, Theory Probab. Appl., 17 (1972), 640–656.10.1137/1117077Search in Google Scholar

[19] Sachkov V. N., “Random mappings with bounded height”, Theory Probab. Appl., 18:1 (1973), 120–130.10.1137/1118009Search in Google Scholar

[20] Sachkov V. N., Combinatorial methods in discrete mathematics, Encyclopedia Math. Appl., 55, Cambridge Univ. Press, Cambridge, 1996, xiii+306 pp.Search in Google Scholar

[21] Sachkov V. N., Probabilistic Methods in Combinatorial Analysis, Cambridge Univ. Press, Cambridge, 1997.10.1017/CBO9780511666193Search in Google Scholar

[22] Sachkov V. N., Introduction to combinatorial methods in discrete mathematics, Moscow: MCCME, 2004 (in Russian).Search in Google Scholar

[23] Seneta E., Regularly Varying Functions, Springer-Verlag, Berlin–Heidelberg–New York, 1976.10.1007/BFb0079658Search in Google Scholar

[24] Timashev A. N., Asymptotic expansions in probabilistic combinatorics, Moscow: "TVP", 2011 (in Russian).Search in Google Scholar

[25] Timashev A. N., Random components in a generalized allocation scheme, Moscow, Akademiya, 2017 (in Russian).Search in Google Scholar

[26] Timashev A. N., “Random mappings with component sizes from a given set”, Theory Probab. Appl., 64:3 (2019), 481–489.10.1137/S0040585X97T989647Search in Google Scholar

[27] Yakimiv A. L., Probabilistic applications of Tauberian theorems,Modern Probability and Statistics,VSP, Leiden, Boston, 2005, viii+225 pp.10.1515/9783110195293Search in Google Scholar

[28] Yakymiv A. L., “On the distribution of the mth maximal cycle lengths of random A-permutations”, DiscreteMath. Appl., 15:5 (2005), 527–546.10.1515/156939205776368931Search in Google Scholar

[29] Yakymiv A. L., “On the number of A-mappings”, Math. Notes, 86:1 (2009), 132–139.10.1134/S0001434609070128Search in Google Scholar

[30] Yakymiv A. L., “A limit theorem for the logarithm of the order of a random A-permutation”, DiscreteMath. Appl., 20:3 (2010), 247-–275.10.1515/dma.2010.015Search in Google Scholar

[31] Yakymiv A. L., “On the number of cyclic points of random A-mapping”, Discrete Math. Appl., 23:5 (2013), 503–515.10.1515/dma-2013-0035Search in Google Scholar

[32] Yakymiv A. L., “On a number of components in a random A-mapping”, Theory Probab. Appl., 59:1 (2015), 114–127.10.1137/S0040585X97986928Search in Google Scholar

[33] Yakymiv A. L., “On the number of components of fixed size in a random A-mapping”, Math. Notes, 97:3 (2015), 468—475.10.1134/S0001434615030177Search in Google Scholar

[34] Yakymiv A. L., “Limit theorems for the logarithm of the order of a random A-mapping”, Discrete Math. Appl., 27:5 (2017), 325–338.10.1515/dma-2017-0034Search in Google Scholar

[35] Yakymiv A. L., “On the order of random permutation with cycle weights”, Theory Probab. Appl., 63:2 (2018), 209–226.10.1137/S0040585X97T989015Search in Google Scholar