20 papers
Algebraic geometric framework of Rogers--Ramanujan identities
Yifeng Huang, Kenny Lau, Ken Ono +1
The Rogers--Ramanujan identities equate a -series whose exponents are governed by a quadratic form with an infinite product supported on two residue classes modulo~. Identiti…
Modularity of Point Counts for the Curves : New Rogers--Ramanujan Identities
Kenny Lau, Ken Ono
For coprime , let be the set of commuting pairs of nilpotent matrices over with . Huang, Jiang, and Oblomkov as…
A bijective proof of a partition theorem of Berkovich and Uncu
Michal Mogielnicki, Ken Ono, Niels Voss +1
In 2016, Berkovich and Uncu proved that, for all nonnegative integers , , and , the number of strict partitions of with odd-indexed odd parts and even-indexed…
On a conjecture of Han and Xiong for fractional Gaussian binomial coefficients
Ken Ono
Han and Xiong recently extended the Gaussian binomial coefficient to positive rational and conjectured that its integer trace, the integer-e…
Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks
Claudia Alfes, Ken Ono, Ashvin Swaminathan
The paper investigates generating functions for higher Dyson ranks, revealing a hidden elliptic structure and providing explicit polynomial obstructions and correction terms that l…
Record compositions of alternating permutations and noncommutative symmetric functions
Evan Chen, Ken Ono, Michal Mogielnicki
The paper determines the exact count of alternating permutations of even length with a given record composition, expressing the numbers using binomial coefficients and Euler number…