The Asymptotic Distribution of the Rank for Unimodal Sequences

K. Bringmann, C. Jennings-Shaffer, and K. Mahlburg, On a Tauberian Theorem of Ingham and Euler-Maclaurin summation

Original

1910

Earlier work this paper cites.

P. Erdös and J. Lehner, The distribution of the number of summands in the partitions of a positive integer , Duke Math. J. 8

1941

Earlier work this paper cites.

A. Ingham, A Tauberian theorem for partitions

1941

Earlier work this paper cites.

F. Dyson, Some guesses in the theory of partitions,

1944

Earlier work this paper cites.

M. Abramowitz and I. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, 55

1964

Earlier work this paper cites.

E. Wright, Stacks. II , Quart. J. Math. Ser. (2) 22

1971

Earlier work this paper cites.

G. Andrews, M. Subbarao, and M. Vidyasagar, A family of combinatorial identities , Canad. Math. Bull. 15

1972

Earlier work this paper cites.

J. Nicolas, Sur les entiers pour lesquels il y a beaucoup de groupes abéliens d’order N N , Ann. Inst. Fourier 28

1978

Earlier work this paper cites.

G. Andrews, Ramanujan’s ”lost” notebook. IV. Stacks and alternating parity in partitions , Adv. in Math. 53

1984

Earlier work this paper cites.

G. Andrews and F. Garvan, Dyson’s crank of a partition

1988

Cited alongside, same era.

F. Garvan, New combinatorial interpretations of Ramanujan’s partition congruences mod 5 , 7 5,7 and 11 11 , Trans. Amer. Math. Soc. 305

1988

Cited alongside, same era.

R. Stanley, Log-concave and unimodal sequences in algebra, combinatorics, and geometry , Graph theory and its applications: East and West (Jinan, 1986), 500–535, Ann. New York Acad. Sci. 576

1989

Cited alongside, same era.

T. Apostol, Modular Functions and Dirichlet Series in Number Theory Series: Grad. Texts Math. 41

1990

Cited alongside, same era.

P. Billingsley, Probability and measure. Third edition. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1995

1995

Cited alongside, same era.

P. Diaconis, S. Janson, and R. Rhoades, Note on a partition limit theorem for rank and crank , Bull. Lond. Math. Soc. 45

2013

Later among the works it cites.

K. Bringmann and K. Mahlburg, Asymptotic formulas for stacks and unimodal sequences

2014

Later among the works it cites.

K. Bringmann, K. Mahlburg, and R. Rhoades, Taylor coefficients of Mock-Jacobi forms and moments of partition statistics

2014

Later among the works it cites.

B. Kim and J. Lovejoy, The rank of a unimodal sequence and a partial theta identity of Ramanujan , Int. J. Number Theory 10

2014

Later among the works it cites.

S. DeSalvo and I. Pak, Log-concavity of the partition function , Ramanujan J. 38

2015

Later among the works it cites.