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pro vyhledávání: '"Xie, Chengfei"'
Autor:
Xie, Chengfei, Ge, Gennian
In this paper, we study problems about the similar configurations in $\mathbb{F}_q^d$. Let $G=(V, E)$ be a graph, where $V=\{1, 2, \ldots, n\}$ and $E\subseteq{V\choose2}$. For a set $\mathcal{E}$ in $\mathbb{F}_q^d$, we say that $\mathcal{E}$ contai
Externí odkaz:
http://arxiv.org/abs/2301.12841
Grassmannian $\mathcal{G}_q(n,k)$ is the set of all $k$-dimensional subspaces of the vector space $\mathbb{F}_q^n.$ Recently, Etzion and Zhang introduced a new notion called covering Grassmannian code which can be used in network coding solutions for
Externí odkaz:
http://arxiv.org/abs/2207.09277
Autor:
Xie, Chengfei, Ge, Gennian
In this paper, we give some new lower bounds for the kissing number of $\ell_p$-spheres. These results improve the previous work due to Xu (2007). Our method is based on coding theory.
Comment: 15 pages, 4 figures; any comments are welcome
Comment: 15 pages, 4 figures; any comments are welcome
Externí odkaz:
http://arxiv.org/abs/2207.09030
Autor:
Xie, Chengfei, Ge, Gennian
Define the superball with radius $r$ and center ${\boldsymbol 0}$ in $\mathbb{R}^n$ to be the set $$ \left\{{\boldsymbol x}\in\mathbb{R}^n:\sum_{j=1}^{m}\left(x_{k_j+1}^2+x_{k_j+2}^2+\cdots+x_{k_{j+1}}^2\right)^{p/2}\leq r^p\right\},0=k_1
Externí odkaz:
http://arxiv.org/abs/2206.05719
Autor:
Xie, Chengfei, Ge, Gennian
Publikováno v:
finite fields and their applications, 79(2022)
We study some sum-product problems over matrix rings. Firstly, for $A, B, C\subseteq M_n(\mathbb{F}_q)$, we have $$ |A+BC|\gtrsim q^{n^2}, $$ whenever $|A||B||C|\gtrsim q^{3n^2-\frac{n+1}{2}}$. Secondly, if a set $A$ in $M_n(\mathbb{F}_q)$ satisfies
Externí odkaz:
http://arxiv.org/abs/2107.03788
Erd\H{o}s posed the problem of finding conditions on a graph $G$ that imply the largest number of edges in a triangle-free subgraph is equal to the largest number of edges in a bipartite subgraph. We generalize this problem to general cases. Let $\de
Externí odkaz:
http://arxiv.org/abs/2102.01338
For a graph $H$ and a $k$-chromatic graph $F,$ if the Tur\'an graph $T_{k-1}(n)$ has the maximum number of copies of $H$ among all $n$-vertex $F$-free graphs (for $n$ large enough), then $H$ is called $F$-Tur\'an-good, or $k$-Tur\'an-good for short i
Externí odkaz:
http://arxiv.org/abs/2102.01332
Autor:
Xie, Chengfei, Ge, Gennian
A Nikodym set $\mathcal{N}\subseteq(\mathbb{Z}/(N\mathbb{Z}))^n$ is a set containing $L\setminus\{x\}$ for every $x\in(\mathbb{Z}/(N\mathbb{Z}))^n$, where $L$ is a line passing through $x$. We prove that if $N$ is square-free, then the size of every
Externí odkaz:
http://arxiv.org/abs/2012.13554
Autor:
Xie, Chengfei, Ge, Gennian
Publikováno v:
In Finite Fields and Their Applications October 2023 91
Autor:
Xie, Chengfei, Ge, Gennian
Publikováno v:
In Finite Fields and Their Applications March 2022 79