Xin-qi Luo

collaborators

2 papers

math.CO2026

Proof of a conjecture on permutations

Yue-Feng She, Xin-Qi Luo

Given a positive integer $n$ , define a function on the symmetric group $S_{n}$ by $F (I ¨ ) = k = 1 \sum n k^{2} I ¨ (k)^{2} .$ Motivated by a conjecture of Zhi-Wei Sun, we investigate the r…

math.NT2026

On the natural density of integers $n$ for which $σ (k n + r_{1}) > σ (k n + r_{2})$

Xin-qi Luo, Chen-kai Ren

For any positive integer $n$ , let $σ (n) = \sum_{d ∣ n} d$ . In 2020, M. Kobayashi and T. Trudgian showed that the natural density of positive integers n with $σ(kn+r_1) \geq σ(kn+r_…

Proof of a conjecture on permutations

On the natural density of integers n for which σ(kn+r1​)>σ(kn+r2​)

On the natural density of integers $n$ for which $σ (k n + r_{1}) > σ (k n + r_{2})$