W.Y.C. Chen, K.Q. Ji and W.J.T. Zang,
Proof of the Andrews-Dyson-Rhoades conjecture on the spt-crank,
Adv. Math. 270 (2015) 60-96.

Cited by

  1. G.E. Andrews, F.J. Dyson and R.C. Rhoades, On the distribution of the spt-crank, Mathematics 1 (2013) 76-88.

  2. S.H. Chan and R. Mao, Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions, Adv. Math. 258 (2014) 414-437.

  3. W.Y.C. Chen, The spt-function of Andrews, In: A. Claesson, M. Dukes, S. Kitaev, D. Manlove and K. Meeks (eds.), Surveys in Combinatorics 2017, 141-203, Cambridge Univ. Press, Cambridge, 2017.

  4. W.Y.C. Chen, K.Q. Ji and W.J.T. Zang, Nearly equal distributions of the rank and the crank of partitions, In: Analytic Number Theory, Modular Forms and q-Hypergeometric Series, 157-177, Springer Proc. Math. Stat. 221, Springer, Cham, 2017.

  5. K.Q. Ji and W.J.T. Zang, Unimodality of the Andrews-Garvan-Dyson cranks of partitions, Adv. Math. 393 (2021) 108053.

  6. B. Kim, On an involution on partitions with crank 0, East Asian Math. J. 35(1) (2019), 9-15.

  7. B. Kim, A remark on tail distributions of partition rank and crank, Bull. Aust. Math. Soc. 93 (2016), 31-36.

  8. R. Mao, Asymptotic formulas for spt-crank of partitions, J. Math. Anal. Appl. 460(1) (2018), 121-139.

  9. R. Mao, Asymptotic inequalities for k-ranks and their cumulation functions, J. Math. Anal. Appl. 409 (2014), 729-741.

  10. R. Mao, On Ranks of Partitions and Congruences of Special Functions, PHD Thesis, Nanyang Technological University, 2014.

  11. R. Mao, On the non-negativity of the spt-crank for partitions without repeated odd parts, J. Number Theory 190 (2018), 72-85.

  12. H. Xiong and W.J.T. Zang, The monotonicity properties for the rank of overpartitions, arXiv:1808.04282.