Anari's Bethe permanent conjecture

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This event attributed to ChatGPT 5.6 Sol Ultra

Anari's Bethe permanent conjecture parent of this event

This event attributed to Dingding Dong

Anari's Bethe permanent conjecture evidence for this event

This event attributed to Vishesh Jain

For every nonnegative $n\times n$ matrix $A$ whose bipartite support graph has girth at least an even integer $g\ge4$, Dong and Jain prove the sharp inequality $$\operatorname{Bethe}(A)\le\operatorname{per}(A)\le2^{2n/g}\operatorname{Bethe}(A).$$ The factor $2^{2n/g}$ is optimal whenever $g\mid2n$, attained by matrices whose support graphs are disjoint unions of $g$-cycles. Thus the result confirms Anari's conjecture, recovers the sharp $2^{n/2}$ universal Anari--Rezaei bound when $g=4$, and approaches exactness as the support-graph girth tends to infinity. parent of this event

VibeMathed record: Anari's Bethe permanent conjecture evidence for this event