Not all cranks

Predators and cranks.

Cranks and T -cores

New statistics on partitions (called cranks) are defined which combinatorially prove Ramanujan’s congruences for the partition function modulo 5, 7, 11, and 25. Explicit bijections are given for the equinumerous crank classes. The cranks are closely related to the t-core of a partition. Using q-series, some explicit formulas are given for the number of partitions which are t-cores. Some related...

Cranks – Really, the Final Problem

A survey of Ramanujan’s work on cranks in his lost notebook is given. We give evidence that Ramanujan was concentrating on cranks when he died, that is to say, the final problem on which Ramanujan worked was cranks – not mock theta functions.

Inequalities Between Ranks and Cranks

Higher moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves the first several cases of (and strengthens) a conjecture due to Garvan, which states that the moments of the crank function are always larger than the moments of the crank f...

Academic nepotism – all that glitters is not gold

Dear Editor With increasing emphasis on publications forfaculty recruitment, career advancementand obtaining research grants, the issues relatedto author kinship and academic nepotism havegrown significantly and these probably reflectthe inflationary growth rather than the optimalgrowth warranted due to increasing researchcomplexity. Allesina S (1) measured the fullmagnitude of nepotism in the ...