arXiv subjects

Guowei Sun

Publications and source records attributed to Guowei Sun.

4 recordsLinked to original sources

arXiv2026

Uniform Tur\'an densities of $k$-uniform hypergraphs

For $k\ge 3$, the $(k-2)$-uniform Tur\'an density $\pi_{k-2}(F)$ of a $k$-graph $F$ is the supremum of $d$ for which there are arbitrarily large $F$-free $k$-graphs that are uniformly $d$-dense with respect to the $k$-vertex cliques of every $(k-2)$-graph on the same vertex set. We develop a \emph{palette framework} for this density. For every family $\mathcal F$ of $k$-graphs, we prove that $\pi_{k-2}(\mathcal F)$ equals the corresponding palette Tur\'an density. We further establish palette classification tools for the existence of $k$-graphs satisfying prescribed palette colorability constraints. Those together allow us to reduce exact density computations to a palette-homomorphism framework without relying on the hypergraph regularity method. As applications, for all $k\ge 3$ and $r\ge 2$, we establish the following values \[ \frac{r-1}{r},\quad \frac{(r-1)^2}{r^2},\quad \frac{r-1}{2r},\quad \frac{(k-1)^k}{k^k},\quad \frac{4(k-2)^{k-2}}{k^k},\quad \frac{4(k-2)^{k-2}}{3k^k} \] as $(k-2)$-uniform Tur\'an densities of single $k$-graphs. Finally, for every $k\ge3$, we show that there exist $k$-graphs $F_1,F_2$ such that \[ \pi_{k-2}(\{F_1,F_2\})< \min\{\pi_{k-2}(F_1),\pi_{k-2}(F_2)\}, \] which provides the first examples of \emph{non-principal} families for this density.

math.CO↗

arXiv2025

Functional inequalities and random walks on increasing subsets of the hypercube

Motivated by random walks on subsets of the hypercube, we prove two discrete functional inequalities on the hypercube by the technique of induction-by-restrictions. First, we give a short, elementary proof of the Poincar\'e inequality on increasing subsets of the cube recently established by Fei and Ferreira Pinto Jr, which yields an $O(n^2)$ upper bound on the mixing time of censored random walks, improving upon previous bounds. Second, adapting Samorodnitsky's induction method to the $p$-biased setting, we establish a sharp $p$-biased edge-isoperimetric inequality for real-valued functions supported on increasing sets, which recovers the classic biased edge-isoperimetric inequality for increasing sets and identifies increasing subcubes as the extremizers. This result also admits a probabilistic interpretation in terms of maximizing the mean first exit time of biased random walks known as Glauber dynamics.

math.CO↗

arXiv2025

Local rainbow colorings of hypergraphs

In this paper, we generalize the concepts related to rainbow coloring to hypergraphs. Specifically, an $(n,r,H)$-local coloring is defined as a collection of $n$ edge-colorings, $f_v: E(K^{(r)}_n) \rightarrow [k]$ for each vertex $v$ in the complete $r$-uniform hypergraph $K^{(r)}_n$, with the property that for any copy $T$ of $H$ in $K^{(r)}_n$, there exists at least one vertex $u$ in $T$ such that $f_u$ provides a rainbow edge-coloring of $T$ (i.e., no two edges in $T$ share the same color under $f_u$). The minimum number of colors required for this coloring is denoted as the local rainbow coloring number $C_r(n, H)$. We first establish an upper bound of the local rainbow coloring number for $r$-uniform hypergraphs $H$ consisting of $h$ vertices, that is, $C_r(n, H)= O\left( n^{\frac{h-r}{h}} \cdot h^{2r + \frac{r}{h}} \right)$. Furthermore, we identify a set of $r$-uniform hypergraphs whose local rainbow coloring numbers are bounded by a constant. A notable special case indicates that $C_3(n,H) \leq C(H)$ for some constant $C(H)$ depending only on $H$ if and only if $H$ contains at most 3 edges and does not belong to a specific set of three well-structured hypergraphs, possibly augmented with isolated vertices. We further establish two 3-uniform hypergraphs $H$ of particular interest for which $C_3(n,H) = n^{o(1)}$. Regarding lower bounds, we demonstrate that for every $r$-uniform hypergraph $H$ with sufficiently many edges, there exists a constant $b = b(H) > 0$ such that $C_r(n,H) = \Omega(n^b)$. Additionally, we obtain lower bounds for several hypergraphs of specific interest.

math.CO↗

arXiv2025

A High-Accuracy SSIM-based Scoring System for Coin Die Link Identification

The analyses of ancient coins, and especially the identification of those struck with the same die, provides invaluable information for archaeologists and historians. Nowadays, these die links are identified manually, which makes the process laborious, if not impossible when big treasures are discovered as the number of comparisons is too large. This study introduces advances that promise to streamline and enhance archaeological coin analysis. Our contributions include: 1) First publicly accessible labeled dataset of coin pictures (329 images) for die link detection, facilitating method benchmarking; 2) Novel SSIM-based scoring method for rapid and accurate discrimination of coin pairs, outperforming current techniques used in this research field; 3) Evaluation of clustering techniques using our score, demonstrating near-perfect die link identification. We provide datasets, to foster future research and the development of even more powerful tools for archaeology, and more particularly for numismatics.

cs.CV↗