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ShowingImportancePrizesTopicCombinatorics
The broad field of discrete mathematics concerned with counting, enumeration, extremal problems, Ramsey theory, designs, and finite structures. General combinatorics claims belong here; additive combinatorics and specific named conjectures carry their own more specific tags.
Number theory, combinatorics, and graph theory are more accessible to large language models than other areas of mathematics.
ContestedCredible evidence or argument exists on multiple sides.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Large language modelsNumber theoryGraph theoryimportance · minorImportance 0.40, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
The packing approach to proving Erdős–Szekeres-type results originates in Seidenberg's 1959 paper.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Discrete geometryHappy ending problemimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
The constant c satisfies c(n) ≥ (1/√2 − o(1))/√n.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Coin-game constantimportance · minorImportance 0.25, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Every sequence of length k(k+3)/2 decomposes into a union of k monotone sequences.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Erdős–Szekeres monotone subsequence theoremimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Every sequence of k^2+1 distinct reals has a monotone subsequence of length k+1, and k^2+1 is optimal.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Erdős–Szekeres monotone subsequence theoremimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
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