Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Jin, Zhihan"'
We prove the following variant of Helly's classical theorem for Hamming balls with a bounded radius. For $n>t$ and any (finite or infinite) set $X$, if in a family of Hamming balls of radius $t$ in $X^n$, every subfamily of at most $2^{t+1}$ balls ha
Externí odkaz:
http://arxiv.org/abs/2405.10275
Many well-studied problems in extremal combinatorics deal with the maximum possible size of a family of objects in which every pair of objects satisfies a given restriction. One problem of this type was recently raised by Alon, Gujgiczer, K\"orner, M
Externí odkaz:
http://arxiv.org/abs/2312.06610
An ordered $r$-matching is an $r$-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of $r$-dimensional orders. The theory of ordered 2-matchings is well-developed and has con
Externí odkaz:
http://arxiv.org/abs/2308.12268
The study of ordered Ramsey numbers of monotone paths for graphs and hypergraphs has a long history, going back to the celebrated work by Erd\H{o}s and Szekeres in the early days of Ramsey theory. In this paper we obtain several results in this area,
Externí odkaz:
http://arxiv.org/abs/2308.04357
In 1993, Fishburn and Graham established the following qualitative extension of the classical Erd\H{o}s-Szekeres theorem. If $N$ is sufficiently large with respect to $n$, then any $N\times N$ real matrix contains an $n\times n$ submatrix in which ev
Externí odkaz:
http://arxiv.org/abs/2305.07003
The graph removal lemma is a fundamental result in extremal graph theory which says that for every fixed graph $H$ and $\varepsilon > 0$, if an $n$-vertex graph $G$ contains $\varepsilon n^2$ edge-disjoint copies of $H$ then $G$ contains $\delta n^{v
Externí odkaz:
http://arxiv.org/abs/2301.13789
Autor:
Jin, Zhihan, Tomon, István
An $r$-uniform hypergraph $H$ is semi-algebraic of complexity $\mathbf{t}=(d,D,m)$ if the vertices of $H$ correspond to points in $\mathbb{R}^{d}$, and the edges of $H$ are determined by the sign-pattern of $m$ degree-$D$ polynomials. Semi-algebraic
Externí odkaz:
http://arxiv.org/abs/2208.01010
Publikováno v:
In Journal of Combinatorial Theory, Series B May 2024 166:203-221
We prove the first superpolynomial lower bounds for learning one-layer neural networks with respect to the Gaussian distribution using gradient descent. We show that any classifier trained using gradient descent with respect to square-loss will fail
Externí odkaz:
http://arxiv.org/abs/2006.12011
The algorithm and complexity of approximating the permanent of a matrix is an extensively studied topic. Recently, its connection with quantum supremacy and more specifically BosonSampling draws special attention to the average-case approximation pro
Externí odkaz:
http://arxiv.org/abs/1911.11962