A.R. Conn, Nick Gould, et al.
Mathematics of Computation
We consider colored partitions of a positive integer n, where the number of times a particular colored part m may appear in a partition of n is equal to the sum of the powers of the divisors of m. An asymptotic formula is derived for the number of such partitions. We also derive an asymptotic formula for the number of partitions of n into c colors. In order to achieve the desired bounds on the minor arcs arising from the Hardy-Littlewood circle method, we generalize a bound on an exponential sum twisted by a generalized divisor function due to Motohashi.
A.R. Conn, Nick Gould, et al.
Mathematics of Computation
Robert Manson Sawko, Malgorzata Zimon
SIAM/ASA JUQ
Richard M. Karp, Raymond E. Miller
Journal of Computer and System Sciences
Jaione Tirapu Azpiroz, Alan E. Rosenbluth, et al.
SPIE Photomask Technology + EUV Lithography 2009