3 papers
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…
math.NT2023
Multimodal sequences and their generating functions
Philip Cuthbertson, Robert Schneider
We define integer multimodal sequences, which are generalizations of unimodal sequences having multiple local peaks of equal size. The generating functions for multimodal sequences…