Xin-qi Luo

activity

20232026

collaborators

5 papers

math.CO2026

A Conjecture on Circular Permutations over Finite Fields

Xin-Qi Luo, Yue-Feng She

Let $\mathbb{F}_q$ be a finite field with $q>7$. Zhi-Wei Sun conjectured that for every $a_0\in\mathbb{F}_q$, there is a circular permutation $(a_1,\dots,a_{q-1})$ of non-z…

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 $F (τ) = k = 1 \sum n k^{2} τ (k)^{2} .$ Motivated by a conjecture of Zhi-Wei Sun, we investigate the res…

math.NT2024

On certain determinants and the square root of some determinants involving Legendre Symbols

Chen-kai Ren, Xin-qi Luo

Let $p > 3$ be a prime and $(\frac{.}{p})$ be the Legendre symbol. For any integer $d$ with $p ∤ d$ and any positive integer $m$ , Sun introduced the determinants $$T_m(d,p)=\det\l…

math.NT2024

Legendre symbols related to $D_{p} (b, 1)$

Xin-Qi Luo, Wei Xia

Let $p$ be an odd prime. For any $b, c \in Z$ , Z.-W. Sun introduced the new-type determinant $D_{p} (b, c) = ∣ (i^{2} + bij + c j^{2})^{p - 2} ∣_{1 ⩽ i, j ⩽ p - 1},$ and studied it…

math.NT2023

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_…