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math.CO2025
Three more proofs of two congruences for Merca's partition function
Fabrizio Zanello
In this note, we provide three new, very short proofs of two interesting congruences for Merca's partition function , which enumerates integer partitions where the odd parts…
math.CO2024
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…
math.CO2023
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…