Yan-Ping Luo

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math.CO2026

The exponent of harmonic LCM avoidance

Yanping Luo, Ruiyi Yang, Keheng Zhu

Fix $k \geq 3$ , and let $f_{k} (N)$ be the largest harmonic sum of a subset of $[N]$ containing no $k$ distinct integers with a common pairwise least common multiple. We prove that $f_k…

math.CO2026

Exterior power sums

Yanping Luo, Ruiyi Yang, Keheng Zhu

We prove that for every fixed $λ > 0$ and all sufficiently large $n$ , any $z_1,\dots,z_n\in\C$ with $∣ z_{j} ∣ \geq 1$ satisfy $max_{2 \leq k \leq n + 1} ∣ \sum_{j} z_{j}^{k} ∣ > e^{- λn}$ . Consequently,…