Yao-Ran Yang

Counterexamples to Charpin's Conjecture on BCH codes

Run Zheng, Yaoran Yang, Yutong Zhang +2

We construct an infinite family of $q$ -ary primitive narrow-sense BCH codes whose minimum distance strictly exceeds the Bose distance; in fact, the gap between the two can be arbit…

math.FA2026

Sharp $p / lo g p$ Bounds for Metric $X_{p}$ Inequalities and Arbitrary Rademacher Chaos

Yutong Zhang, Yaoran Yang

Naor proved that $L_{p}$ satisfies the metric $X_{p}$ inequality with the sharp scaling parameter and asked for the optimal dependence of its constant on $p$ . The best previously known…

The 196560 auxiliary-function conjecture for the Leech lattice

Yutong Zhang, Yaoran Yang

Cohn and Kumar conjectured in 2009 that there is a radial Schwartz function $g : R^{24} \to R$ satisfying $g (r) \leq 0$ for $r \geq 6$ , $g (r) \geq 0$ for $r \geq 0$ , $g(2)…

math.AG2026

Frobenius-orbit slicing and uniform elimination of positive-dimensional singular loci

Yutong Zhang, Yaoran Yang

Let $\cX\subseteq\Pj^n_{\Z}$ be a fixed integral quasiprojective subscheme, smooth over $Z$ of relative dimension $r$ . For each fixed $m \geq 1$ , we bound the probability that the $m…

Exact Minimum Distance of the Ding--Li--Xia Cyclic Codes

Yutong Zhang, Yaoran Yang

The cyclic codes $℧ (q, m, h)$ introduced by Ding, Li, and Xia form a nonbinary generalization of punctured binary Reed--Muller codes. Ding, Li, and Xia established the bounds $(q^…

math.AG2026

Hyperplane anti-Bertini embeddings over finite fields

Yutong Zhang, Yaoran Yang

Baker asked, as recorded by Poonen, whether a fixed smooth quasiprojective variety over a finite field must have a smooth rational hyperplane section after every sufficiently high-…

math.MG2026

Finite and Urysohn obstructions to Sabok's S-prime simplex questions

Yutong Zhang, Yaoran Yang

Sabok asked whether the compact convex set $S'(X)$ attached to a separable metric space of diameter at most one is always a simplex, and whether $S'(\mathbb U_1)$ is the Poulse…

The least non-partitionable zero-sum subset for zero-sum triples in finite abelian groups

Yutong Zhang, Yaoran Yang

Let $G$ be a finite abelian group, and let $μ(G)$ denote the least size of a subset $S\subseteq G$ with $3\mid |S|$, total sum zero, and no partition into zero-sum triples;…

A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant

Yaoran Yang, Gaishi Yang, Yutong Zhang

Let $p \geq 7$ be a prime with $p \equiv 3 (mod 4)$ and let $χ$ be the Legendre symbol modulo $p$ . We prove that $\det[x+χ(j-k)]_{0\le j,k\le(p-7)/2}=\floor{(p-2)/3}^{2}x$ in $\mathbb{C}[…

cs.DS2026

One-Shot Klein Cutting Planes for Lipschitz Geodesically Convex Optimization in Hyperbolic Space

Yutong Zhang, Yaoran Yang, Yifan Zhu +1

Motivated by the COLT 2023 open problem of Criscitiello, Martínez-Rubio, and Boumal on deterministic first-order methods for Lipschitz geodesically convex optimization on Hadamard…

A Uniform Random-Lattice Tail Bound for the SVP Kissing-Profile Parameter

Yutong Zhang, Yaoran Yang

A recent SICOMP paper on classical and quantum algorithms for the shortest vector problem introduced a lattice-dependent parameter $γ(L)$, bounded universally in the exponential…

math.CA2026

Weighted Uniform Endpoint Majorants for Integrals Involving Modified Bessel Functions

Yaoran Yang, Yutong Zhang

We give an affirmative full-range solution to Gaunt's 2019 Open Problem~2.10. The problem asks whether, for every $ν>-1/2$ and $0<γ<1$, the reciprocal-power integral \(\int_0^x…

math.GR2026

A compensation theorem for the Sylow-integral invariant and counterexamples to an \texorpdfstring{ $A_{5}$ }{A5}-characterization conjecture

Yutong Zhang, Yaoran Yang

Let $ν_p(G)$ be the number of Sylow $p$-subgroups of a finite group $G$, let $σ_p(G)$ be their common order, and set \[ γ(G)=\int_0^1\sum_{p\inπ(G)}ν_p(G)x^{σ_p(G)}\,dx =\s…

math.GR2026

Finite factorization is detected by undermonoids

Yutong Zhang, Yaoran Yang

Let $M$ be a cancellative commutative monoid and call a submonoid $S$ of $M$ an undermonoid if $\G(S)=\G(M)$ inside the Grothendieck group of $M$ . Gotti and Li asked whether the fi…

A Local Valuation Criterion for Quadratic-Permutation Interleaved Zadoff--Chu Sequences

Yutong Zhang, Yaoran Yang

Berggren and Popović introduced quadratic-permutation-polynomial interleaved Zadoff--Chu sequences and, from exhaustive data, conjectured that all normalized QPP-interleaved Zadoff…

Two determinant evaluations in Sun's conjectures involving Legendre symbols

Yaoran Yang, Yutong Zhang

We prove two determinant evaluations attached to Sun's conjectures on matrices of Legendre symbols. The first one resolves the $p\equiv1\pmod4$ part of Conjecture 4.8(i) by reduc…

Sun-type determinant and permanent congruences

Yaoran Yang, Yutong Zhang

Sun proposed a list of congruence and quadratic-residue conjectures for determinants and permanents over residue classes modulo a prime. This article gives a uniform treatment of C…

A Determinant Congruence Conjectured by Sun

Yutong Zhang, Yaoran Yang

We prove a strengthened form of a conjecture of Sun on a determinant attached to a binary quadratic form. Let $n > 3$ and let $c, d \in Z$ . If $n$ is composite, then \[ \det\big[(i^2+c…

Algebraic Resolutions of Seven Open Problems on Cyclic and Negacyclic Codes Supporting Designs

Yutong Zhang, Yaoran Yang

This paper gives a unified algebraic solution to seven open problems of Wang, Tang and Ding on cyclic, negacyclic and constacyclic codes supporting designs. For the cyclic code \[…

Intermediate Constacyclic Codes and Scalar-Residue Reed--Muller Layers

Yaoran Yang, Yutong Zhang

A 2024 paper of Sun, Ding and Wang introduced a second class of constacyclic codes over finite fields, denoted $C (q, m, r, ℓ)$ , with length $(q^{m} - 1) / r$ , where $r ∣ (q - 1)$ and the…

Betti Numbers of Cut Complexes of Squared Paths and a Recurrence Conjecture

Yutong Zhang, Yaoran Yang

For a graph $G$ on $[n]$ , the $k$ -cut complex $Δ_{k} (G)$ has facets $[n] ∖ T$ , where $T$ ranges over the $k$ -subsets that induce disconnected subgraphs of $G$ . Bayer, Denker,…

Excess Obstructions and Layer-Contained Certificates for the Hypergraph Nash--Williams--Tutte Conjecture

Yutong Zhang, Yaoran Yang

Guo, Li, Shangguan, Tamo, and Wootters proposed a hypergraph analogue of the Nash--Williams--Tutte theorem, asserting that every $k$ -weakly-partition-connected hypergraph admits a…