3 problems

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Moore's conjecture on the maximizers of the second-moment function
Let $g_{{G(n,m)}}$ be the function arising in the second-moment analysis of balanced $k$ -colorings of $G(n,m)$ , defined on the overlap matrices $\{\alpha_{ij}\}$ . Moore's conjectur…
Conjectureopengraph-coloring random-graphs second-moment-methodarXiv posted 2 days ago
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Small-density second-moment conjecture for average-case matrix discrepancy
Small-density second-moment conjecture. When $\kappa$ approaches $2$ , the range in which the second-moment ratio remains bounded by a constant may include values of $\tau$ arbitrar…
Conjectureopenmatrix-discrepancy random-matrices second-moment-methodarXiv posted 2 days ago
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Conjecture on the second-moment asymptotic for spanning trees in random regular graphs
The second-moment conjecture.
Conjectureopenrandom-regular-graphs second-moment-method spanning-treesarXiv posted 2 days ago

Moore's conjecture on the maximizers of the second-moment function