3 papers
math.NT2025
An Orthogonal View of Gaußian Polynomials
Christian Krattenthaler, Brandt Kronholm, Paul Marsh
We establish an alternative, ``perpendicular" collection of generating functions for the coefficients of Gaussian polynomials, . We provide a…
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…
math.CO2015
A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins
Felix Breuer, Brandt Kronholm
The main result of this paper is a bijective proof showing that the generating function for partitions with bounded differences between largest and smallest part is a rational func…