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pro vyhledávání: '"Chao, Ting"'
Autor:
Chao, Ting-Wei, Yu, Hung-Hsun Hans
The Kruskal--Katona theorem determines the maximum number of $d$-cliques in an $n$-edge $(d-1)$-uniform hypergraph. A generalization of the theorem was proposed by Bollob\'as and Eccles, called the partial shadow problem. The problem asks to determin
Externí odkaz:
http://arxiv.org/abs/2410.06498
Let $P$ be a $2n$-point set in the plane that is in general position. We prove that every red-blue bipartition of $P$ into $R$ and $B$ with $|R| = |B| = n$ generates $\Omega(n^{3/2})$ red-red-blue empty triangles.
Comment: 9 pages, 3 figures
Comment: 9 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/2409.17078
Autor:
Chao, Ting-Wei, Yu, Hung-Hsun Hans
In this short note, we present a purely entropic proof that in a $3$-edge-colored simple graph with $R$ red edges, $G$ green edges, and $B$ blue edges, the number of rainbow triangles is at most $\sqrt{2RGB}$.
Comment: 5 pages, 5 figures
Comment: 5 pages, 5 figures
Externí odkaz:
http://arxiv.org/abs/2407.14084
Autor:
Chao, Ting-Wei, Yu, Hung-Hsun Hans
A joint of a set of lines $\mathcal{L}$ in $\mathbb{F}^d$ is a point that is contained in $d$ lines with linearly independent directions. The joints problem asks for the maximum number of joints that are formed by $L$ lines. Guth and Katz showed that
Externí odkaz:
http://arxiv.org/abs/2307.15380
Autor:
Chao, Ting-Wei, Yu, Hung-Hsun Hans
In this paper, we investigate several extremal combinatorics problems that ask for the maximum number of copies of a fixed subgraph given the number of edges. We call problems of this type Kruskal--Katona-type problems. Most of the problems that will
Externí odkaz:
http://arxiv.org/abs/2307.15379
Publikováno v:
Virology Journal, Vol 21, Iss 1, Pp 1-5 (2024)
Abstract Tetraparvovirus is an emerging parvovirus infecting a variety of mammals and humans, and associated with human diseases including severe acute respiratory infection and acute encephalitis syndrome. In the present study, a Tetraparvovirus ung
Externí odkaz:
https://doaj.org/article/7b7349859cbb4e6fb64ae07114efb1d1
Autor:
Chao, Ting-Wei, Yu, Hung-Hsun Hans
Publikováno v:
In Journal of Combinatorial Theory, Series B November 2024 169:480-506
Autor:
Chao, Ting-Wei, Dong, Zichao
Publikováno v:
Electronic Journal of Combinatorics, vol. 29(3), P3.59, 2022
We give a new unified proof that any simple graph on $n$ vertices with maximum degree at most $\Delta$ has no more than $a\binom{\Delta+1}{t}+\binom{b}{t}$ cliques of size $t \ (t \ge 3)$, where $n = a(\Delta+1)+b \ (0 \le b \le \Delta)$.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/2201.05181
Autor:
Bukh, Boris, Chao, Ting-Wei
Publikováno v:
Discrete Analysis, 2021:26
A Kakeya set in $\mathbb{F}_q^n$ is a set containing a line in every direction. We show that every Kakeya set in $\mathbb{F}_q^n$ has density at least $1/2^{n-1}$, matching the construction by Dvir, Kopparty, Saraf and Sudan.
Comment: 9 pages, 1
Comment: 9 pages, 1
Externí odkaz:
http://arxiv.org/abs/2108.00074
Autor:
Lawton, Savannah M., Manson, Megan A., Fan, Meng-Ni, Chao, Ting-Yen, Chen, Chun-Yu, Kim, Peter, Campbell, Carley, Cai, Xiaohe, Vander Kooi, Amber, Miao, Carol H.
Publikováno v:
In Molecular Therapy 3 April 2024 32(4):969-981