Xin-qi Luo

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20232026

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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…