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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.CO2025
-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…
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…