The Maximum of per(I−A) in Odd Order

Yair Lavi

For odd n=2k+1>1 and doubly stochastic A, Lavi proves max per(I−A)=3·2^(k−2). Every maximizer is a simultaneous permutation conjugate of the half-weight triangle block plus k−1 swap blocks.

Sources for this record

What was already known

Kim and Roush gave the block candidate, a row-stochastic upper bound 2^k and the n=3 case. The doubly stochastic maximum and equality cases for n≥5 remained open.

AI involvement AI-led

Yair Lavi guided the project and wrote the paper. He credits GPT-5.6 Sol and Claude Fable 5 jointly with carrying out the proof; their individual steps are not separated.

The author expressly says the two models carried out the proof under his guidance.

Importance Notable

The proof settles the odd-order maximum and characterizes equality cases.

Limitations

Lavi reports reviewing the model-produced arguments, but does not describe a complete rigorous check of the full proof.

Technical verification Partial

Lavi reports reviewing the resulting proof arguments, but does not specify a completed rigorous check of the entire maximum and equality classification. The source-reported human review is recorded only at its documented scope.

Independent checking

Author review of the resulting proof arguments

Checker
Yair Lavi
Scope
The model-produced arguments for the Kim–Roush maximum and equality cases
Basis
Reported by the linked checker
Evidence source

Human understanding Full

The author's paper explains the functional-digraph expansion, top-layer charge bound and support argument classifying equality.

Correction and publication history