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math.CO2026
A perimeter analogue of Franklin's identity and an inequality related to the parity of parts
Philip Cuthbertson
We prove two conjectures regarding partition perimeter inequalities. It was conjectured by Gray, Payne, and Watson that Franklin's partition identity becomes an eventual inequality…
math.CO2026
A requested analytic proof of an identity of Dixit, Kumar, and Srivastava
Philip Cuthbertson
Recently Dixit, Kumar, and Srivastava investigated what they called Rascoe and non-Rascoe partitions. These are defined to be the set of distinct partitions where the length of the…