arXiv subjects

Ji Young Kim

Publications and source records attributed to Ji Young Kim.

6 recordsLinked to original sources

arXiv2026

Tight universality of $m$-gonal forms with minimal criterion sets

For integers $m\geq3$ and $n\geq1$, an $m$-gonal form is called tight $\mathcal{T}(n)$-universal if it represents exactly the positive integers $\mathcal{T}(n)=\{ n, n+1, n+2, \ldots \}$. In this paper, we study the minimal criterion set $\mathrm{CS}(m,n)$ for tight $\mathcal{T}(n)$-universality. Our main result determines $\mathrm{CS}(m,n)$ for $n \geq8$, $3 \leq m \leq \left\lfloor \frac{3n+1}{2} \right\rfloor$, except for $(m,n)=(7,9)$ and $(7,10)$. More precisely, $$ \mathrm{CS}(m,n)= \begin{cases} \{ n, n+1, \ldots, 2n-1 \}, & m=5, \newline \{ n, n+1, \ldots, 2n \}, & m\neq5. \end{cases} $$ We also establish the corresponding tight $\mathcal{T}(n)$-universality results and show that the upper bound on $m$ is optimal.

math.NT↗

arXiv2026

Online Monitoring and Corrective Steering of Programming Agents

Fixing GitHub issues in large-scale projects is a long-horizon task, especially when a fix requires changes across multiple locations or the issue description lacks the information needed to localize and repair it. As a result, agents traverse long trajectories that are prone to inefficiency and error: they drift away from their intended plan, repeat failed actions, or terminate without a working patch. This paper proposes LivePlan to monitor, detect, and correct such behavioral inefficiencies and drifts in real time. LivePlan decouples judging from advising: a deterministic, rule-based monitor examines general signals over the trajectory to detect issues without invoking an LLM, and only when an issue is detected does it consult an advisor LLM for a high-level, next-step correction. This design avoids the misleading re-planning and costly interventions of prior approaches. We implement LivePlan on top of SWE-agent and evaluate it using five LLMs (three as executor agents and two as advisors) across SWE-bench Verified and SWE-bench Pro. Compared to vanilla SWE-agent, LivePlan notably improves issue resolution rates, achieving consistent gains of up to 15.2% (average: 9.9%), while incurring only an additional cost of $0.08 per instance. The additional solutions concentrate on medium and hard instances. LivePlan consistently outperforms alternative approaches in resolution rate, with minimal regression on already successful runs and new successes on problems that no baseline solves.

cs.SE↗

arXiv2019

Integral Quadratic Forms Avoiding Arithmetic Progressions

For every positive integer k, it is shown that there exists a positive definite diagonal quaternary integral quadratic form that represents all positive integers except for precisely those which lie in k arithmetic progressions. For k=1, all forms with this property are determined.

math.NT↗

arXiv2009

Even universal binary Hermitian lattices over imaginary quadratic fields

A positive definite even Hermitian lattice is called \emph{even universal} if it represents all even positive integers. We introduce a method to get all even universal binary Hermitian lattices over imaginary quadratic fields $\Q{-m}$ for all positive square-free integers $m$ and we list optimal criterions on even universality of Hermitian lattices over $\Q{-m}$ which admits even universal binary Hermitian lattices.

math.NT↗

arXiv2008

The Fifteen Theorem for Universal Hermitian Lattices over Imaginary Quadratic Fields

We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields over $\mathbb{Q}(\sqrt{-m})$ for all m. For each imaginary quadratic field $\mathbb{Q}(\sqrt{-m})$, we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13,14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneeberger's fifteen theorem and ours is the number 13.

math.NT↗

arXiv2008

Binary normal regular Hermitian lattices over imaginary quadratic fields

We call a positive definite Hermitian lattice regular if it represents all integers which can be represented locally by the lattice. We investigate binary regular Hermitian lattices over imaginary quadratic fields $\mathbb{Q}(\sqrt{-m})$ and provide a complete list of the (normal) Hermitian lattices.

math.NT↗