[1]Andrews, G. E. (1998) The Theory of Partitions, Cambridge Mathematical Library, Cambridge University Press.

[2]Apostol, T. M. (1990) Modular Functions and Dirichlet Series in Number Theory, second edition, Vol. 41 of Graduate Texts in Mathematics, Springer.

[3]Brennan, C., Knopfmacher, A. and Wagner, S. (2008) The distribution of ascents of size *d* or more in partitions of *n*. Combin. Probab. Comput. 17 495–509.

[4]Corteel, S., Pittel, B., Savage, C. and Wilf, H. (1999) On the multiplicity of parts in a random partition. Random Struct. Alg. 14 185–197.

[5]Erdős, P. and Lehner, J. (1941) The distribution of the number of summands in the partitions of a positive integer. Duke Math. J. 8 335–345.

[6]Flajolet, P., Gourdon, X. and Dumas, P. (1995) Mellin transforms and asymptotics: Harmonic sums. Theoret. Comput. Sci. 144 3–58.

[7]Flajolet, P. and Odlyzko, A. (1990) Singularity analysis of generating functions. SIAM J. Discrete Math. 3 216–240.

[8]Flajolet, P. and Sedgewick, R. (2009) Analytic Combinatorics, Cambridge University Press.

[9]Goh, W. M. Y. and Schmutz, E. (1995) The number of distinct part sizes in a random integer partition. J. Combin. Theory Ser. A 69 149–158.

[10]Grabner, P. J. and Knopfmacher, A. (2006) Analysis of some new partition statistics. Ramanujan J. 12 439–454.

[11]Han, G.-N. (2008) An explicit expansion formula for the powers of the Euler product in terms of partition hook lengths. arXiv:0804.1849v3 [math.CO]

[12]Husimi, K. (1938) Partitio numerorum as occurring in a problem of nuclear physics. In Proc. Physico-Mathematical Society of Japan 20 912–925.

[13]Hwang, H.-K. and Yeh, Y.-N. (1997) Measures of distinctness for random partitions and compositions of an integer. Adv. Appl. Math. 19 378–414.

[14]Kessler, I. and Livingston, M. (1976) The expected number of parts in a partition of *n*. Monatsh. Math. 81 203–212.

[15]Knopfmacher, A. and Munagi, A. O. (2009) Successions in integer partitions. Ramanujan J. 18 239–255.

[16]Knopfmacher, A. and Warlimont, R. (2006) Gaps in integer partitions. Util. Math. 71 257–267.

[17]Mutafchiev, L. R. (2005) On the maximal multiplicity of parts in a random integer partition. Rama-nu-jan J. 9 305–316.

[18]Rademacher, H. (1973) Topics in Analytic Number Theory (Grosswald, E., Lehner, J. and Newman, M., eds), Vol. 169 of *Die Grundlehren der Mathematischen Wissenschaften*, Springer.

[19]Ralaivaosaona, D. (2012) On the distribution of multiplicities in integer partitions. Ann. Combin. 16 871–889.

[20]Richmond, L. B. (1974/75) The moments of partitions I. Acta Arith. 26 411–425.

[21]Stanley, R. P. (1997) Enumerative Combinatorics 1, Vol. 49 of *Cambridge Studies in Advanced Mathematics*, Cambridge University Press.

[22]Szekeres, G. (1990) Asymptotic distribution of partitions by number and size of parts. In Number Theory I: Budapest 1987, Vol. 51 of *Colloq. Math. Soc. János Bolyai*, North-Holland, pp. 527–538.

[23]Szpankowski, W. (2001) Average Case Analysis of Algorithms on Sequences, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience.

[24]Wagner, S. (2006) A class of trees and its Wiener index. Acta Appl. Math. 91 119–132.

[25]Wagner, S. (2009) On the distribution of the longest run in number partitions. Ramanujan J. 20 189–206.

[26]Wagner, S. (2011) Limit distributions of smallest gap and largest repeated part in integer partitions. Ramanujan J. 25 229–246.

[27]Watson, G. N. (1995) A Treatise on the Theory of Bessel Functions, Cambridge Mathematical Library. Cambridge University Press. Reprint of the second (1944) edition.