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· 2026 · arXiv 2602.00680

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Multiplicity for partially ordered sets

math.CO · 2026-07-01 · unverdicted · novelty 7.0

Proves the exact Ramsey number R^arith_2 equals 9 for monochromatic triples in E_n of B_n and establishes 2^{δn+o(n)} ≤ M^arith_2(B_n) ≤ 2^{γn+o(n)} with explicit entropy constants δ≈1.356779 and γ≈1.567837.

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  • Multiplicity for partially ordered sets math.CO · 2026-07-01 · unverdicted · none · ref 27

    Proves the exact Ramsey number R^arith_2 equals 9 for monochromatic triples in E_n of B_n and establishes 2^{δn+o(n)} ≤ M^arith_2(B_n) ≤ 2^{γn+o(n)} with explicit entropy constants δ≈1.356779 and γ≈1.567837.