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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3 Pith papers cite this work. Polarity classification is still indexing.
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math.CO 3years
2026 3verdicts
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Introduces weak and strong poset Ramsey-Turán numbers for t-chains in the Boolean lattice and proves equality to (k-1)(l-1) for chains when t=1 plus Theta(n^t) growth for non-chains.
The paper proves existence of strong Boolean Ramsey numbers R^#_k,t(B|Q) for any finite poset Q and gives probabilistic upper bounds plus combinatorial lower bounds on the strong Erdős-Gyárfás function f_t^#(n,p,q).
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Multiplicity for partially ordered sets
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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Ramsey-Tur\'{a}n theory for partially-ordered sets
Introduces weak and strong poset Ramsey-Turán numbers for t-chains in the Boolean lattice and proves equality to (k-1)(l-1) for chains when t=1 plus Theta(n^t) growth for non-chains.
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Erd\H{o}s-Gy\'{a}rf\'{a}s problem for partially ordered sets
The paper proves existence of strong Boolean Ramsey numbers R^#_k,t(B|Q) for any finite poset Q and gives probabilistic upper bounds plus combinatorial lower bounds on the strong Erdős-Gyárfás function f_t^#(n,p,q).