Sharp lower bound on the spectral gap of biased adjacent-transposition chains on the symmetric group is established, resolving Fill's conjecture with characterization of minimizers and eigenvalue multiplicity.
Transposition is nearly optimal for iid list update
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AI agents exploring Platonic mathematical structures via proof hypergraphs may reveal the overall architecture of formal mathematics and what makes parts of it human-accessible.
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Spectral gap of biased adjacent-transposition chains
Sharp lower bound on the spectral gap of biased adjacent-transposition chains on the symmetric group is established, resolving Fill's conjecture with characterization of minimizers and eigenvalue multiplicity.
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Artificial Intelligence and the Structure of Mathematics
AI agents exploring Platonic mathematical structures via proof hypergraphs may reveal the overall architecture of formal mathematics and what makes parts of it human-accessible.