bibkey: xu2020polyhedral authors: Yibo Xu, Warren Adams, and Akshay Gupte year: 2020 title: Polyhedral Analysis of Symmetric Multilinear Polynomials over Box Constraints doi: null url: https://arxiv.org/abs/2012.06394v2 claim: Symmetric multilinear convex and concave envelopes over a common box supply the quadratic and cubic upper chords and the four-factor lower facet consumed by the constant-suspension separator. strata_touched:

• D5/S3/Observer/ProbabilisticClosure/TrajectoryLaws/ConstantSuspensionSeparator license: arXiv non-exclusive distribution license; mathematical citation only triage: anchor

Scope

The source is https://arxiv.org/abs/2012.06394v2, Theorem 5.1, equations (31)–(32), and Corollary 4.3. On a positive common box with endpoints L and H, the product’s upper envelope gives the quadratic and cubic chord bounds after taking expectations with common coordinate mean. The four-coordinate lower facet at the vertex type with three coordinates equal to H is

$$\prod _{i=0}^3{x}_i\ge L{H}^2\left(\sum _{i=0}^3{x}_i-L-2H\right).$$

The separator consumes these classical inequalities at L=3/5 and H=2/3. It proves the finite instances by exact polynomial factorizations and nonnegative box terms. These helpers are not new general inequalities. The literature result does not identify the finite generator’s complete laws with its unweighted stationary circulation, nor does it supply the complete-law endpoint separation constant.

The paper is cited for mathematics; no source text or software is copied.

Verified locator

https://arxiv.org/abs/2012.06394v2