3 papers
math.CO2026
Fixed Perimeter Analogues of Several Partition Results Related to Parity
Gabriel Gray, Emily Payne, Holly Swisher +1
In 2016, Straub proved that Euler's classic partition identity holds true for partitions with largest hook (perimeter) . This inspired further study of the relationship between…
math.CO2025
Fixed perimeter analogues of some partition results
Gabriel Gray, Emily Payne, Holly Swisher +1
Euler's partition identity states that the number of partitions of into odd parts is equal to the number of partitions of into distinct parts. Strikingly, Straub proved in…
math.NT2024
A generalization of Franklin's partition identity and a Beck-type companion identity
Gabriel Gray, David Hovey, Brandt Kronholm +3
Euler's classic partition identity states that the number of partitions of into odd parts equals the number of partitions of into distinct parts. We develop a new generaliz…