## My Publications

### 1/k-Eulerian Polynomials and k-Inversion Sequences

with Jun Ma, Shi-Mei Ma, and Yeong-Nan YehThe Electronic Journal of Combinatorics, 2019

In this paper, we provide a bijective proof that the ascent number over k-inversion sequences of length n is equidistributed with a weighted variant of the ascent number of permutations of order n.

### On Convex Holes in d-dimensional Point Sets

with Boris Bukh and Ron HolzmanCombinatorics, Probability and Computing, 2021

Given a finite set A of points in R^d, we say that points a_1,a_2,…,a_k in A form an k-hole in A if they are the vertices of a convex polytope, which contains no points of A in its interior. We construct arbitrarily large point sets in general position in  R^d having no holes of size O(4^d*d*log d) or more.

### Sharp Density Bounds on the Finite Field Kakeya Problem

with Boris BukhDiscrete Analysis, 2021

A Kakeya set in F_q^n is a set containing a line in every direction. We show that every Kakeya set in F_q^n has density at least 1/2^{n−1}, matching the construction by Dvir, Kopparty, Saraf and Sudan.

### Empty Axis-Parallel Boxes

with Boris BukhInternational Mathematics Research Notices, 2022

We show that, for every set of n points in the d-dimensional unit cube, there is an empty axis-parallel box of volume at least Ω(d/n) as n→∞ and d is fixed. In the opposite direction, we give a construction without an empty axis-parallel box of volume O(d^2*log d/n)⁠.

### Digital Almost Nets

with Boris BukhThe Electronic Journal of Combinatorics, 2022

Digital nets (in base 2) are the subsets of [0,1]^d that contain exactly the expected number of points in every not-too-small dyadic box. We construct finite sets, which we call "almost nets", such that every such dyadic box contains almost the expected number of points from the set, but whose size is exponentially smaller than the one of nets. We also establish a lower bound on the size of such almost nets.

### A Simple Proof of the Gan-Loh-Sudakov Conjecture

with Zichao DongThe Electronic Journal of Combinatorics, 2022

Gan, Loh, and Sudakov conjectured that the graph on n vertices with maximum degree at most ∆ that maximizing the number of t-cliques is a disjoint union of many ∆+1 cliques and a smaller clique. They also proved that the conjecture in true for all t>3 if it's true for t=3. Chase proved the case t=3. In this paper, we simplified and generalized the proof of Chase and give a unified proof for all t>=3.

### Several Improved Asymptotic Normality Criteria and Their Applications to Graph Polynomials

with Zhibin Du and Yeong-Nan YehDiscrete Mathematics, 2023

In this paper we present an improved asymptotic normality criterion, along with several variant versions, which usually just ask for one coefficient of the generating function, without knowing any roots. In virtue of these new criteria, the asymptotic normality of some usual combinatorial statistics can be revealed and extended. Among which, we introduce the applications to matching numbers and Laplacian coefficients in detail.

### Kruskal--Katona-Type Problems via Entropy Method

with Hung-Hsun Hans YuarXiv

Using the entropy method, we prove that, in a 3-colored graph with R red, G green, B blue edges, the number of rainbow triangles is at most (2RGB)^{1/2}, which is sharp. Also, we give a generalization of the Kruskal--Katona theorem that implies many other previous generalizations.

### Tight Bound and Structural Theorem for Joints

with Hung-Hsun Hans YuarXiv

A joint of a set of lines in F^d is a point that is contained in d lines with linearly independent directions. We proved that the construction given by taking the joints and the lines to be all the d-wise intersections and all the (d−1)-wise intersections of M hyperplanes in general position is the only optimal (with least lines) if the number of joints is M choose d.