12 papers
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…
Formalizing multi-graded Brenner-Schröer Proj schemes and dilatations of rings in Lean4
Arnaud Mayeux, Jujian Zhang
We present a detailed formalization in Lean4 of some multigraded algebraic geometry constructions, focusing on the Brenner--Schröer Proj construction and algebraic dilatations of…
Parity of -differentials in genus zero and one
Dawei Chen, Evan Chen, Kenny Lau +2
Here we completely determine the spin parity of -differentials with prescribed zero and pole orders on Riemann surfaces of genus zero and one. This result was previously obtaine…
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…