GPT-5.5 Pro helps prove new ESP inequalities in an arXiv combinatorics paper
lihua_lei_stat · x · 2026-07-28
A new arXiv preprint by Yanjun Han and Jonathan Niles-Weed proves new inequalities for elementary symmetric polynomials on centered vectors and zero-row/zero-column matrices.
What the paper claims
- It gives new bounds for ESPs in two centered settings: vectors that sum to zero and square matrices with zero row and column sums.
- The results are used to derive a unified upper bound for the mean-field approximation guarantee of permutation mixtures.
- The paper also states a sharp chi^2 version of the de Finetti theorem for finite sequences over a small alphabet.
Extra note
- The abstract says the main proof ideas were developed by the GPT-5.5 Pro model.
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