Separating hash families are useful combinatorial structures that generalize several well-studied objects in cryptography and coding theory. Let $p_t(N, q)$ denote the maximum size of the universe for a $t$-perfect hash family of length $N$ over an alphabet of size $q$. We show that $q^{2 – o(1)} < p_t(t, q) = o(q^2)$ for all $t \ge 3$, thereby resolving an open problem raised by Blackburn et al. (2008) for certain parameter ranges. Previously, this result was known only for $t = 3$ and $t = 4$. Our approach establishes the existence of a large set of integers that avoids nontrivial solutions to a system of correlated linear equations. This is joint work with Xiande Zhang and Gennian Ge.
Welcome Eero Räty, Xiaofan Yuan, and Xin Wei, new members of IBS ECOPRO
The IBS Discrete Mathematics Group welcomes Dr. Eero Räty, Dr. Xiaofan Yuan, and Dr. Xin Wei, new research fellows at the IBS Extremal Combinatorics and Probability Group, starting January 1, 2026.
Dr. Eero Räty received his Ph.D. from the University of Cambridge under the supervision of Prof. Imre Leader. Until recently, he was a postdoctoral researcher at Umeå University, Sweden. He is interested in extremal and probabilistic combinatorics.
Dr. Xiaofan Yuan received her Ph.D. from the Georgia Institute of Technology under the supervision of Prof. Xingxing Yu. She is interested in graph theory and extremal combinatorics. Until recently, she was a postdoctoral researcher at Arizona State University.
Dr. Xin Wei received his Ph.D. from the University of Science and Technology of China under the supervision of Prof. Xiande Zhang. His research interests include combinatorics, coding theory, and graph theory and their interactions.