Yue-Feng She

activity

20202026

collaborators

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

math.NT2026

Representations of positive integers by three almost-prime squares

Yue-Feng She, Yu-Chen Sun, Guang-Liang Zhou

Let $P_{r}$ denote an integer with at most $r$ prime factors, counted with multiplicity. It is known that every sufficiently large integer $N$ satisfying $N \equiv 3 (mod 24)$ and $…

math.NT2025

On restricted sums of four squares and Zhi-Wei Sun's $x + 24 y$ conjecture

Hai-Liang Wu, Yue-Feng She

In this paper, by using the arithmetic theory of ternary quadratic forms, we study some refinements on Lagrange's four-square theorem. For example, given positive integers $a, b$ sa…

math.NT2024

Some determinants involving binary forms

Yue-Feng She, Zhi-Wei Sun

In this paper, we study arithmetic properties of certain determinants involving powers of $i^{2} + c ij + d j^{2}$ , where $c$ and $d$ are integers. For example, for any odd integer $n > 1$ wit…

math.CO2022

A novel permanent identity with applications

Yue-Feng She, Zhi-Wei Sun, Wei Xia

Let $n$ be a positive integer, and define the rational function $S (x_{1}, \dots, x_{2 n})$ as the permanent of the matrix $[x_{j, k}]_{1 \leq j, k \leq 2 n}$ , where $$x_{j,k}=\begin{cases}(x_…

math.NT2022

Additive decompositions of cubes in finite fields