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For an integer $h\geq2$, an edge-ordered $h$-uniform hypergraph $H^<$ is an $h$-uniform hypergraph with a linear ordering of its hyperedges. For an integer $q \geq 1$, the edge-ordered Ramsey number $R_{\mathrm{edge}}(H^<;q)$ of $H^<$ is the smallest positive integer $N$ such that there exists an edge-ordered $h$-unifo...
Bozano is described, a multi-agent open-source system that uses parallel prover agents with a verifier agent and maintains a human-readable research state that solves open problems and answers four questions raised in the papers.
We provide a general upper bound on multicolor ordered Ramsey numbers in terms of the interval chromatic number and the degeneracy of an ordered graph. We extend previous results by Conlon, Fox, Lee, and Sudakov (2017) by showing that for every $n$-vertex ordered graph $G^<$ with degeneracy $d\geq2$, and interval chrom...
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