C. Yip

activity

20222026

most citedExact values and improved bounds on

k

-neighborly families of boxes

1 citations · 3 across the 13 of their papers we have counts for

collaborators

13 papers

math.NT2026

The Prouhet--Tarry--Escott problem for subsets with small doubling in integral domains

Ernie Croot, Junzhe Mao, Chi Hoi Yip

The Prouhet--Tarry--Escott (PTE) problem has many generalizations and has been studied in various algebraic domains. In this paper, we prove that finite subsets $S$ of integral dom…

math.RA2026

Positivity preservers over finite fields II

Dominique Guillot, Himanshu Gupta, Prateek Kumar Vishwakarma +1

We say that a matrix over a finite field $F_{q}$ is positive definite if it is symmetric and each of its leading principal minors is a nonzero square in $F_{q}$ . In p…

math.NT2026

A sharp inverse theorem for the quadratic large sieve

Ernie Croot, Chi Hoi Yip, Junzhe Mao +1

We prove that if $A \subseteq [N]$ , $∣ A ∣ ≫ N$ , and $∣ A_{p} ∣ \leq p /2 + O (1)$ for every prime $p ≪ lo g N$ , then $A$ contains at least $exp (c lo g N / lo g lo g N)$ el…

math.NT2026

An absolute bound for generalized Diophantine tuples over polynomial rings

Kin Ming Tsang, Chi Hoi Yip

Let $F$ be an algebraically closed field of characteristic $0$ . Let $k \geq 2$ be an integer, and let $n \in F [x] ∖ {0}$ . We study generalized Diophantine tup…

math.NT2026

A combinatorial large sieve for Sidon sets, distances, and norm forms

Ernie Croot, Junzhe Mao, Cosmin Pohoata +2

We develop a new combinatorial large sieve method for sets with bounded algebraic multiplicities. The method exploits algebraic splitting modulo many small primes: local congruence…

math.NT2026

Hilbert cubes in sets with arithmetic properties

Ernie Croot, Junzhe Mao, Chi Hoi Yip

In this paper, we introduce new general frameworks for estimating the maximal dimension of Hilbert cubes contained in finite truncations of arbitrary sets. As applications, we inve…

math.NT2025

An inverse theorem on sets with rich additive structure modulo primes

Ernie Croot, Junzhe Mao, Chi Hoi Yip

In this paper, we prove several results on the structure of maximal sets $S \subseteq [N]$ such that $S$ mod $p$ is contained in a short arithmetic progression, or the union of sho…

math.NT2025

Diophantine tuples and product sets in shifted powers

Ernie Croot, Chi Hoi Yip

Let $k \geq 2$ and $n \neq = 0$ . A Diophantine tuple with property $D_{k} (n)$ is a set of positive integers $A$ such that $ab + n$ is a $k$ -th power for all $a, b \in A$ with $a \neq = b$ . Such…

math.CO2025

Uniform set systems with small VC-dimension

Ting-Wei Chao, Zixiang Xu, Chi Hoi Yip +1

We investigate the longstanding problem of determining the maximum size of a $(d + 1)$ -uniform set system with VC-dimension at most $d$ . Since the seminal 1984 work of Frankl and Pac…

math.CO2024★ 1 cited

The Frankl-Pach upper bound is not tight for any uniformity

Gennian Ge, Zixiang Xu, Chi Hoi Yip +2

For any positive integers $n \geq d + 1 \geq 3$ , what is the maximum size of a $(d + 1)$ -uniform set system in $[n]$ with VC-dimension at most $d$ ? In 1984, Frankl and Pach initiated the s…

math.CO2023★ 1 cited

Exact values and improved bounds on $k$ -neighborly families of boxes

Xinbu Cheng, Meiqin Wang, Zixiang Xu +1

A finite family $F$ of $d$ -dimensional convex polytopes is called $k$ -neighborly if $d - k \leq dim (C \cap C^{'}) \leq d - 1$ for any two distinct members $C,C'\in\mathcal{F}…

math.CO2022★ 1 cited

Sperner systems with restricted differences

Zixiang Xu, Chi Hoi Yip

Let $F$ be a family of subsets of $[n]$ and $L$ be a subset of $[n]$ . We say $F$ is an $L$ -differencing Sperner system if $∣ A ∖ B ∣ \in L$ for any distinct…

math.CO2022

Intersective sets over abelian groups

Zixiang Xu, Chi Hoi Yip

Given a finite abelian group $G$ and a subset $J \subset G$ with $0 \in J$ , let $D_{G} (J, N)$ be the maximum size of $A \subset G^{N}$ such that the difference set $A - A$ and $J^{N}$ ha…

The Prouhet--Tarry--Escott problem for subsets with small doubling in integral domains

Positivity preservers over finite fields II

A sharp inverse theorem for the quadratic large sieve

An absolute bound for generalized Diophantine tuples over polynomial rings

A combinatorial large sieve for Sidon sets, distances, and norm forms

Hilbert cubes in sets with arithmetic properties

An inverse theorem on sets with rich additive structure modulo primes

Diophantine tuples and product sets in shifted powers

Uniform set systems with small VC-dimension

The Frankl-Pach upper bound is not tight for any uniformity

Exact values and improved bounds on k-neighborly families of boxes

Sperner systems with restricted differences

Intersective sets over abelian groups

Exact values and improved bounds on $k$ -neighborly families of boxes