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English(EN) Exact values and exact upper bounds for families of integers with arithmetic progression intersections (Erd\H{o}s Problem #272)

数学论文解决 Erdős 问题 #272 关于整数族

作者 PulseAugur 编辑部 · [1 个来源] ·

一篇新论文解决了 Erdős 问题 #272，重点关注具有算术进展交集的整数族。研究人员确定了大小最多为 12 的整数族的精确值，证实了一个猜想，即此类集合的最大数量为 $\binom{N}{2}+1+\lfloor(N-1)/4\rfloor$。该工作还建立了极值族的结构约束，并证明了 Szabo 的下界对于具有共同元素的族来说是精确的。 AI

排序理由 关于组合数学问题的学术论文。[lever_c_demoted from research: ic=1 ai=0.0]

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数学论文解决 Erdős 问题 #272 关于整数族

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关于组合数学问题的学术论文。[lever_c_demoted from research: ic=1 ai=0.0]
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报道来源 [1]

  1. arXiv cs.AI TIER_1 English(EN) · Zhanfu Yang ·

    具有算术进展交集的整数族的精确值和精确上界（Erdős 问题 #272）

    arXiv:2607.23004v1 Announce Type: cross Abstract: Let $t(N)$ be the largest $t$ for which there exist distinct sets $A_1,\dots,A_t \subseteq \{1,\dots,N\}$ such that $A_i \cap A_j$ is a nonempty arithmetic progression for all $i \neq j$ (Erdos Problem #272). Simonovits and Sos pr…

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