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<p>A Boolean lattice of dimension <i>n</i>, denoted <i>Q</i><sub><i>n</i></sub>, is the power set of an <i>n</i>-element ground set <i>X</i> equipped with inclusion relation. For posets <i>P</i><sub>1</sub>, …, <i>P</i><sub><i>k</i></sub>, the Boolean Ramsey number R<sub><i>k</i></sub>(<i>P</i><sub>1</sub>, …, <i>P</i><sub><i>k</i></sub>) is the smallest integer <i>N</i> such that for any <i>k</i>-coloring of the sets of <i>Q</i><sub><i>N</i></sub>, there exists a copy of <i>P</i><sub><i>i</i></sub> with color <i>i</i>. In this paper, we study the exact values or give upper and lower bounds of multicolor Boolean Ramsey numbers for some known posets and poset products.</p>

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Multicolor Boolean Ramsey Numbers

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Ao Tan,
  • Gang Yang,
  • Ya-ping Mao

摘要

A Boolean lattice of dimension n, denoted Qn, is the power set of an n-element ground set X equipped with inclusion relation. For posets P1, …, Pk, the Boolean Ramsey number Rk(P1, …, Pk) is the smallest integer N such that for any k-coloring of the sets of QN, there exists a copy of Pi with color i. In this paper, we study the exact values or give upper and lower bounds of multicolor Boolean Ramsey numbers for some known posets and poset products.