C. Yip

activity

20212026

most citedAn annotated bibliography for comparative prime number theory

5 citations · 24 across the 23 of their papers we have counts for

collaborators

23 papers

math.NT2026

Additive decompositions of multiplicative subgroups via differential identities

Chi Hoi Yip, Albert Cochrane, Semin Yoo

We develop a local-to-global differential framework for additive decomposition problems involving multiplicative subgroups of prime fields. Starting from Hanson--Petridis-type auxi…

cs.IT2026

Asymptotic Bounds on Generalized Covering Radii of Binary Primitive BCH Codes

Maosheng Xiong, Chi Hoi Yip, Ferdinando Zullo

Fix integers $e \geq 2$ and $r \geq 1$ . In this paper we study the $r$ -th generalized covering radius $ρ_{r} (B C H (e, m))$ of the binary primitive $e$ -error-correcting BCH code $BC…

math.NT2026

Multiplicative subgroups are not restricted sumsets

Chi Hoi Yip, Semin Yoo

We determine exactly which proper multiplicative subgroups of a prime field can be represented as a restricted sumset of the form $A\mathbin{\widehat{+}} A=\{a+a':a,a'\in A,\ a\ne…

math.NT2026

Extensions of the Carlitz-McConnel and Blokhuis-Sziklai theorems for unions of cyclotomic classes

Maosheng Xiong, Chi Hoi Yip

Let $p$ be a prime, let $q = p^{n}$ , and let $D \subseteq F_{q}^{*}$ . A celebrated result of Carlitz and McConnel states that if $D$ is a proper subgroup of $F_{q}^{*}$ ,…

cs.IT2026

On generalized covering radii of binary primitive double-error-correcting BCH codes

Maosheng Xiong, Chi Hoi Yip

The generalized covering radii (GCR) of linear codes are a fundamental higher-dimensional extension of the classical covering radius. While the second and third GCR of binary primi…

math.CO2026

Multiplicative irreducibility of shifted multiplicative subgroups

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

In a recent breakthrough, Kalmynin resolved conjectures of Lev--Sonn and Sárközy on additive decompositions of multiplicative subgroups of prime fields. In this paper, inspired by…

math.CO2026

Product representations of polynomials over finite fields

Hyunwoo Lee, Chi Hoi Yip, Semin Yoo

Erdős, Sárközy, and Sós studied the asymptotics of the maximum size of a subset of ${1, 2, \dots, N}$ such that it does not contain $k$ distinct elements whose product is a perfec…

math.CO2026

Paley-type matrices and $1$ -factorizations of complete graphs

Chi Hoi Yip, Semin Yoo, Shikang Yu

Ball, Ortega--Moreno, and Prodromou asked two questions about whether, for every odd prime $p$ , one can find a $1$ -factor of the complete graph $K_{p + 1}$ with some arithmetic restr…

math.NT2025

Bipartite Diophantine tuples and their applications

Kin Ming Tsang, Chi Hoi Yip

This paper investigates bipartite variants of generalized Diophantine tuples and their applications. We generalize a result of Bugeaud--Dujella on a special family of bipartite Dio…

math.CO2025

Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields, II

Chi Hoi Yip

The well-known Van Lint--MacWilliams' conjecture states that if $q$ is an odd prime power, and $A \subseteq F_{q^{2}}$ such that $0, 1 \in A$ , $∣ A ∣ = q$ , and $a - b$ is a square f…

math.CO2025

$f$ -Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

We investigate $f$ -Diophantine sets over finite fields via new explicit constructions of families of quasi-random hypergraphs from multivariate polynomials. In particular, our cons…

math.NT2025★ 1 cited

Multiplicative irreducibility of small perturbations of the set of shifted $k$ -th powers

Chi Hoi Yip

Motivated by a conjecture of Erdős on the additive irreducibility of small perturbations of the set of squares, recently Hajdu and Sárközy studied a multiplicative analogue of the…

math.NT2024

Oscillation results for the summatory functions of fake mu's

Greg Martin, Chi Hoi Yip

Mossinghoff, Trudgian, and the first author~\cite{MMT23} recently introduced a family of arithmetic functions called ``fake $μ$ 's'', which are multiplicative functions for which th…

math.NT2024★ 2 cited

$F$ -Diophantine sets over finite fields

Chi Hoi Yip, Semin Yoo

Let $k \geq 2$ , $q$ be an odd prime power, and $F \in F_{q} [x_{1}, \dots, x_{k}]$ be a polynomial. An $F$ -Diophantine set over a finite field $F_{q}$ is a set $A \subset…

math.CO2024

Paley-like quasi-random graphs arising from polynomials

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

Paley graphs and Paley sum graphs are classical examples of quasi-random graphs. In this paper, we provide new constructions of families of quasi-random graphs that behave like Pal…

math.NT2024★ 1 cited

On cyclotomic matrices involving Gauss sums over finite fields

Hai-Liang Wu, Jie Li, Li-Yuan Wang +1

Inspired by the works of L. Carlitz and Z.-W. Sun on cyclotomic matrices, in this paper, we investigate certain cyclotomic matrices involving Gauss sums over finite fields, which c…

math.NT2024★ 3 cited

Explicit constructions of Diophantine tuples over finite fields

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

A Diophantine $m$ -tuple over a finite field $F_{q}$ is a set ${a_{1}, \dots, a_{m}}$ of $m$ distinct elements in $F_{q}^{*}$ such that $a_{i} a_{j} + 1$ is a square in $…

math.NT2024★ 2 cited

Distribution of power residues over shifted subfields and maximal cliques in generalized Paley graphs

Greg Martin, Chi Hoi Yip

We derive an asymptotic formula for the number of solutions in a given subfield to certain system of equations over finite fields. As an application, we construct new families of m…

math.NT2023★ 3 cited

Multiplicatively reducible subsets of shifted perfect $k$ -th powers and bipartite Diophantine tuples

Chi Hoi Yip

Recently, Hajdu and Sárközy studied the multiplicative decompositions of polynomial sequences. In particular, they showed that when $k \geq 3$ , each infinite subset of $\{x^k+1: x…

math.NT2023★ 3 cited

Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples

Seoyoung Kim, Chi Hoi Yip, Semin Yoo

In this paper, we investigate the multiplicative structure of a shifted multiplicative subgroup and its connections with additive combinatorics and the theory of Diophantine equati…

math.NT2023★ 5 cited

An annotated bibliography for comparative prime number theory

Greg Martin, Pu Justin Scarfy Yang, Aram Bahrini +9

The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory (through mid-2024) together with a summary of its results. We…

math.NT2023★ 2 cited

Additive decompositions of large multiplicative subgroups in finite fields

Chi Hoi Yip

We show that a large multiplicative subgroup of a finite field $F_{q}$ cannot be decomposed into $A + A$ or $A + B + C$ nontrivially. We also find new families of multiplicative s…

math.NT2021★ 2 cited

Asymptotics for the number of directions determined by $[n] \times [n]$ in $F_{p}^{2}$

Greg Martin, Ethan Patrick White, Chi Hoi Yip

Let $p$ be a prime and $n$ a positive integer such that $\frac{p}{2} + 1 \leq n \leq p$ . For any arithmetic progression $A$ of length $n$ in $F_{p}$ , we establish…

Additive decompositions of multiplicative subgroups via differential identities

Asymptotic Bounds on Generalized Covering Radii of Binary Primitive BCH Codes

Multiplicative subgroups are not restricted sumsets

Extensions of the Carlitz-McConnel and Blokhuis-Sziklai theorems for unions of cyclotomic classes

On generalized covering radii of binary primitive double-error-correcting BCH codes

Multiplicative irreducibility of shifted multiplicative subgroups

Product representations of polynomials over finite fields

Paley-type matrices and 1-factorizations of complete graphs

Bipartite Diophantine tuples and their applications

Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields, II

f-Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials

Multiplicative irreducibility of small perturbations of the set of shifted k-th powers

Oscillation results for the summatory functions of fake mu's

F-Diophantine sets over finite fields

Paley-like quasi-random graphs arising from polynomials

On cyclotomic matrices involving Gauss sums over finite fields

Explicit constructions of Diophantine tuples over finite fields

Distribution of power residues over shifted subfields and maximal cliques in generalized Paley graphs

Multiplicatively reducible subsets of shifted perfect k-th powers and bipartite Diophantine tuples

Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples

An annotated bibliography for comparative prime number theory

Additive decompositions of large multiplicative subgroups in finite fields

Asymptotics for the number of directions determined by [n]×[n] in Fp2​

Paley-type matrices and $1$ -factorizations of complete graphs

$f$ -Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials

Multiplicative irreducibility of small perturbations of the set of shifted $k$ -th powers

$F$ -Diophantine sets over finite fields

Multiplicatively reducible subsets of shifted perfect $k$ -th powers and bipartite Diophantine tuples

Asymptotics for the number of directions determined by $[n] \times [n]$ in $F_{p}^{2}$