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Math paper solves Erdős Problem #272 on integer families

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A new paper addresses Erdős Problem #272, focusing on families of integers with arithmetic progression intersections. Researchers have determined the exact values for families of size up to 12, confirming a conjecture that the maximum number of such sets is $\binom{N}{2}+1+\lfloor(N-1)/4\rfloor$. The work also establishes structural constraints on extremal families and proves that Szabo's lower bound is exact for families with a common element. AI

RANK_REASON Academic paper on a combinatorial mathematics problem. [lever_c_demoted from research: ic=1 ai=0.0]

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Math paper solves Erdős Problem #272 on integer families

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Academic paper on a combinatorial mathematics problem. [lever_c_demoted from research: ic=1 ai=0.0]
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COVERAGE [1]

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

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