Andrew V. Sills
Published 2020-01-27Version 1
The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of $n$ is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartiitons is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of \emph{Mathematica} are presented along with results of a test for their numerical accuracy.
Comments: 18 pp., this version incorporates corrections to the published version suggested to the author by Michael Schlosser in an email dated January 20, 2020
Journal: Gems in Experimental Mathematics, ed. T. Amdeberhan, L. Medina, and V. Moll; Contemporary Mathematics 517 (2010) 321--338
Partitions weighted by the parity of the crank
Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions
Asymptotic formulas for the number of the partitions into summands of the form $\lfloorαm\rfloor$
![QR code for arXiv:2001.09568 [math.NT]](http://oss.arxitics.com/images/favicon.svg)