3 citations · 8 across the 13 of their papers we have counts for
13 papers
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…
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…
Multiplicative irreducibility of shifted multiplicative subgroups in the extremal case
Semin Yoo
In a recent breakthrough, Kalmynin proved a conjecture of Sárközy on additive irreducibility of the set of quadratic residues in a prime field. More recently, Kim, Yip, and Yoo ini…
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…
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 such that it does not contain distinct elements whose product is a perfec…
Paley-type matrices and -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 , one can find a -factor of the complete graph with some arithmetic restr…
Sphere intersections and incidences over finite fields
Doowon Koh, Ben Lund, Chuandong Xu +1
We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We ob…
-Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
We investigate -Diophantine sets over finite fields via new explicit constructions of families of quasi-random hypergraphs from multivariate polynomials. In particular, our cons…
-Diophantine sets over finite fields
Chi Hoi Yip, Semin Yoo
Let , be an odd prime power, and be a polynomial. An -Diophantine set over a finite field is a set $A \subset…
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…
Explicit constructions of Diophantine tuples over finite fields
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
A Diophantine -tuple over a finite field is a set of distinct elements in such that is a square in $…
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…
Intersection patterns and connections to distance problems
Thang Pham, Semin Yoo
Let and be sets in a finite vector space. In this paper, we study the magnitude of the set , where runs through a set of transformations. More precisely, we…