Minc's permanent upper-bound conjecture

Let MM be an n×nn\times n matrix with entries in {0,1}\{0,1\} and row sums d1,,dnd_1,\dotsc,d_n. Minc's conjecture. The permanent of MM is at most

i=1n(di!)1/di.\prod_{i=1}^n (d_i!)^{1/d_i}.

Minc's conjecture was proved by Brégman and later given a shorter proof by Schrijver, so the conjecture is now a theorem.

Sources & referencesView supporting material

Primary source

Wojciech Samotij, “Entropy methods in combinatorics”, arXiv:2607.24414 (2026).

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