6 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…
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 rational f…
Formalizing Curve Neighborhoods in Lean 4
Yihe Huang, Sizhe Cui, Jiaqi Wang +1
Combinatorial curve neighborhoods are somewhat foundational when setting up the quantum Schubert calculus for affine flag manifolds. In the specific case of type , you c…
Dead ends in square-free digit walks
Evan Chen, Chris Cummins, Ben Eltschig +18
We study "dead ends" in square-free digit walks: square-free integers such that, in base , every one-digit extension is non-square-free. In base , the stochastic…
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_…