Zobrazeno 1 - 10
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pro vyhledávání: '"Pham, A. Tuan"'
Automatic Heuristic Design (AHD) is an active research area due to its utility in solving complex search and NP-hard combinatorial optimization problems in the real world. The recent advancements in Large Language Models (LLMs) introduce new possibil
Externí odkaz:
http://arxiv.org/abs/2412.14995
Autor:
Pham, Huy Tuan
Expectation thresholds arise from a class of integer linear programs (LPs) that are fundamental to the study of thresholds in large random systems. An avenue towards estimating expectation thresholds comes from the fractional relaxation of these inte
Externí odkaz:
http://arxiv.org/abs/2412.03540
Autor:
Pham, Huy Tuan, Zakharov, Dmitrii
A set of integers $A$ is non-averaging if there is no element $a$ in $A$ which can be written as an average of a subset of $A$ not containing $a$. We show that the largest non-averaging subset of $\{1, \ldots, n\}$ has size $n^{1/4+o(1)}$, thus solvi
Externí odkaz:
http://arxiv.org/abs/2410.14624
We study the number of monochromatic solutions to linear equations in a $2$-coloring of $\{1,\ldots,n\}$. We show that any nontrivial linear equation has a constant fraction of solutions that are monochromatic in any $2$-coloring of $\{1,\ldots,n\}$.
Externí odkaz:
http://arxiv.org/abs/2410.13758
Autor:
Nenadov, Rajko, Pham, Huy Tuan
Combining ideas of Pham, Sah, Sawhney, and Simkin on spread perfect matchings in super-regular bipartite graphs with an algorithmic blow-up lemma, we prove a spread version of the blow-up lemma. Intuitively, this means that there exists a probability
Externí odkaz:
http://arxiv.org/abs/2410.06132
Autor:
Nenadov, Rajko, Pham, Huy Tuan
We present a short and simple proof of the celebrated hypergraph container theorem of Balogh--Morris--Samotij and Saxton--Thomason. On a high level, our argument utilises the idea of iteratively taking vertices of largest degree from an independent s
Externí odkaz:
http://arxiv.org/abs/2408.08514
A family of $r$ distinct sets $\{A_1,\ldots, A_r\}$ is an $r$-sunflower if for all $1 \leqslant i < j \leqslant r$ and $1 \leqslant i' < j' \leqslant r$, we have $A_i \cap A_j = A_{i'} \cap A_{j'}$. Erd\H{o}s and Rado conjectured in 1960 that every f
Externí odkaz:
http://arxiv.org/abs/2408.04165
We present an explicit subset $A\subseteq \mathbb{N} = \{0,1,\ldots\}$ such that $A + A = \mathbb{N}$ and for all $\varepsilon > 0$, \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\in A^2\big\}\big|}{N^{\varepsilon}} = 0.\] T
Externí odkaz:
http://arxiv.org/abs/2405.08650
We initiate the systematic study of the following Tur\'an-type question. Suppose $\Gamma$ is a graph with $n$ vertices such that the edge density between any pair of subsets of vertices of size at least $t$ is at most $1 - c$, for some $t$ and $c > 0
Externí odkaz:
http://arxiv.org/abs/2405.05902
Autor:
Conlon, David, Fox, Jacob, He, Xiaoyu, Mubayi, Dhruv, Pham, Huy Tuan, Suk, Andrew, Verstraëte, Jacques
Answering a question of Erd\H{o}s and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive integers each at most $n$ is $2^{(c_x + o(1))n}$ for an explicit const
Externí odkaz:
http://arxiv.org/abs/2404.16016