20 citations · 37 across the 20 of their papers we have counts for
27 papers
A bijection for partitions simultaneously -regular and -distinct
William J. Keith
In this note a bijection is constructed between the set of partitions of n simultaneously s-regular and t-distinct, and those simultaneously t-regular and s-distinct. Some implicat…
Schmidt-type theorems for partitions with uncounted parts
George E. Andrews, William J. Keith
Schmidt's theorem is significantly generalized, to partitions in which periodic but otherwise arbitrary subsets of parts are counted or uncounted. The identification of such sets o…
Parity of the coefficients of certain eta-quotients
William J. Keith, Fabrizio Zanello
We investigate the parity of the coefficients of certain eta-quotients, extensively examining the case of -regular partitions. Our theorems concern the density of their odd valu…
Restricted k-color partitions, II
William J. Keith
We consider -colored partitions, partitions in which colors exist but at most colors may be chosen per size of part. In particular these generalize overpartitions. A…
Binary compositions and semi-Pell compositions
William J. Keith, Augustine O. Munagi
In analogy with the semi-Fibonacci partitions studied recently by Andrews, we define semi-Pell compositions and semi--Pell compositions. We find that these are in bijection with…
Partitions into parts simultaneously regular, distinct, and/or flat
William J. Keith
We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by , appearing fewer than times, or differing by…