Jujian Zhang

collaborators

12 papers

math.CO2026

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 $i$ , $j$ , and $n$ , the number of strict partitions of $n$ with $i$ odd-indexed odd parts and $j$ even-indexed…

cs.LO2026

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 r…

math.CO2026

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…

math.CO2026

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 $λ$ , and studied rational f…

math.RT2026

Chebyshev quotients, Demazure multiplicities, and Dyck-path models

Rekha Biswal, Ken Ono, Jujian Zhang

We study Chebyshev quotients that arise in the representation theory of Lie algebras, specifically within the theory of Demazure flags for fusion products of $sl_{2} [t]$ -m…

math.CO2026

Formalizing $A_{1}^{(1)}$ 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 $A_{1}^{(1)}$ , you c…

math.NT2026

ABC implies that Ramanujan's tau function misses almost all primes

David Kurniadi Angdinata, Evan Chen, Chris Cummins +21

Lehmer conjectured that Ramanujan's tau-function never vanishes. In a related direction, a folklore conjecture asserts that infinitely many primes arise as absolute values of Raman…

math.DS2026

On the paucity of lattice triangles

David Kurniadi Angdinata, Evan Chen, Ken Ono +3

A rational triangle $T$ (one whose angles are rational multiples of $π$ ) unfolds to a translation surface $X_{T}$ . The lattice triangle problem asks to classify those $T$ for which…

math.CO2026

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 $N$ such that, in base $b$ , every one-digit extension $b N + d$ is non-square-free. In base $10$ , the stochastic…

math.NT2026

Almost all primes are partially regular

Evan Chen, Chris Cummins, Ben Eltschig +18

For odd primes $p$ , we let $K_{p} := Q (ζ_{p})$ be the $p$ th cyclotomic field and let $ω$ denote its Teichmuller character. For $α > 1/2$ , we say that an odd prime $p$ is partially…

math.NT2026

Parity of $k$ -differentials in genus zero and one

Dawei Chen, Evan Chen, Kenny Lau +2

Here we completely determine the spin parity of $k$ -differentials with prescribed zero and pole orders on Riemann surfaces of genus zero and one. This result was previously obtaine…

math.CO2026

Fel's Conjecture on Syzygies of Numerical Semigroups

Evan Chen, Chris Cummins, GSM +18

Let $S = ⟨ d_{1}, \dots, d_{m} ⟩$ be a numerical semigroup and $k [S]$ its semigroup ring. The Hilbert numerator of $k [S]$ determines normalized alternating syzygy power sums $K_…

A bijective proof of a partition theorem of Berkovich and Uncu

Formalizing multi-graded Brenner-Schröer Proj schemes and dilatations of rings in Lean4

A problem of Andrews and Dhar on partitions

Reciprocals of Partition Polynomials

Chebyshev quotients, Demazure multiplicities, and Dyck-path models

Formalizing A1(1)​ Curve Neighborhoods in Lean 4

ABC implies that Ramanujan's tau function misses almost all primes

On the paucity of lattice triangles

Dead ends in square-free digit walks

Almost all primes are partially regular

Parity of k-differentials in genus zero and one

Fel's Conjecture on Syzygies of Numerical Semigroups

Formalizing $A_{1}^{(1)}$ Curve Neighborhoods in Lean 4

Parity of $k$ -differentials in genus zero and one