Dyson's rank, crank and adjoint

This page is a short list of references on the subject.

Papers by Freeman Dyson:

F.J. Dyson, Some guesses in the theory of partitions, Eureka (Cambridge), vol. 8 (1944), 10-15.
The .jpg files of pages: 10-11, 12-13, 14-15 or a single .pdf file.
F.J. Dyson, Problems for Solution: 4261, Amer. Math. Monthly, vol. 54 (1947), 418.
F.J. Dyson, A new symmetry of partitions, Journal Combinatorial Theory, vol. 7 (1969), 56-61.
F.J. Dyson, A walk through Ramanujan's garden, In Ramanujan revisited (Urbana-Champaign, Ill., 1987), pp. 7--28, Academic Press, Boston, MA, 1988.
F.J. Dyson, Mappings and symmetries of partitions. Journal Combinatorial Theory (Ser. A), vol. 51 (1989), 169-180.

Papers by other authors:

N.J. Fine, Some new results on partitions, Proc. Nat. Acad. Sci. USA vol. 34 (1948), 616-618.
A.O.L. Atkin and P. Swinnerton-Dyer, Some properties of partitions, Proc. London Math. Soc. (3), vol. 4 (1954), 84--106.
F.G. Garvan, New combinatorial interpretations of Ramanujan's partition congruences mod 5, 7 and 11, Trans. Amer. Math. Soc. vol. 305 (1988), 47-77.
G.E. Andrews and F.G. Garvan, Dyson's crank of a partition, Bull. Amer. Math. Soc. (N.S.), vol. 18 (1988), 167-171.
F. Garvan, D. Kim, and D. Stanton, Cranks and t-cores, Invent. Math. vol. 101 (1990), 1-17.
A. Berkovich and F. Garvan, Some observations on Dyson's new symmetries of partitions, J. Combin. Theory (Ser. A), vol. 100 (2002), 61-93.
I. Pak, On Fine's partition theorems, Dyson, Andrews, and missed opportunities, Math. Intelligencer, vol. 25 (2003), 10-16.
A.O.L. Atkin and F. Garvan, Relations between the ranks and cranks of partitions, Ramanujan Journal, vol. 7 (2003), 343-366.
C. Boulet and I. Pak, A combinatorial proof of the Rogers-Ramanujan identities, J. Combin. Theory (Ser. A), vol. 113 (2006), 1019-1030.
K. Bringmann and K. Ono, The f(q) mock theta function conjecture and partition ranks, Inventiones Mathematicae, vol. 165 (2006), 243-266.
G.E. Andrews and K. Ono, Ramanujan's congruences and Dyson's crank, Proc. NAS USA, vol. 102 (2005), 15277.
K. Mahlburg, Partition congruences and the Andrews–Garvan–Dyson crank, Proc. NAS USA, vol. 102 (2005), 15373-15376.

The famous phone call:

See Chapter 10 in The work of George Andrews: a Madison perspective by Richard Askey, in "The Andrews Festschrift (Maratea, 1998)", Sem. Lothar. Combin. vol. 42 (1999), Art. B42b, 24 pp.

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Last updated 8/20/2008