6 papers
Partitions with parity restrictions: a bijective approach
William Keith, Bruce E. Sagan
There has been recent interest in integer partitions whose parts satisfy parity restrictions: for example, those where all the odd parts are distinct, or those where all the even p…
On a conjecture of Andrews and Bachraoui
Koustav Banerjee, Kathrin Bringmann, William J. Keith
Recently, Andrews and Bachraoui considered a generating function associated with certain two-color partitions, and conjectured that this function has non-negative coef…
Combinatorial proof of a congruence for partitions into two sizes of part
Eli R. DeWitt, William J. Keith
Previous work showed that, for the number of partitions of into exactly two part sizes, one has . The earlier proof required the techn…
Reciprocals of false theta functions
William J. Keith
We investigate reciprocals of false theta functions, producing results such as congruences, simple asymptotic bounds, and combinatorial identities. Of particular interest is a conn…
Parity of the coefficients of certain eta-quotients, III: two special classes
William J. Keith, Fabrizio Zanello
We continue a series of papers studying the parity of families of eta-quotients, which provide implications for the parity of the partition function as well as an overarching conje…
Parity of the coefficients of certain eta-quotients, II: The case of even-regular partitions
William J. Keith, Fabrizio Zanello
We continue our study of the density of the odd values of eta-quotients, here focusing on the -regular partition functions for even. Based on extensive computational e…