From the 3 of 20 linked papers with an AI index.
7 papers · 1 filter
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…
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…
Fel's Conjecture on Syzygies of Numerical Semigroups
Evan Chen, Chris Cummins, GSM +18
Let be a numerical semigroup and its semigroup ring. The Hilbert numerator of determines normalized alternating syzygy power sums $K_…
A problem of Andrews and Dhar on partitions
Simon Mahns, Ken Ono, Jujian Zhang
This paper is motivated by a broad question about AI-assisted mathematics: can an AI system help discover and certify an explicit bijection between two infinite sequences of compli…
Reciprocals of Partition Polynomials
Evan Chen, Ken Ono, Jujian Zhang
Ballantine--Beck--Feigon--Maurischat introduced the subsum polynomial \[ \operatorname{sp}(λ,x):=\prod_i (1+x^{λ_i}) \] attached to an integer partition , and studied rationa…