REVIEW 1 cited by
On moments of a polytope
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P in R^d is a rational function. Its denominator is the product of linear forms dual to the vertices of P raised to the power equal to the degree of the density function. Using this, we solve the inverse moment problem for the set of, not necessarily convex, polytopes having a given set S of vertices. Under a weak non-degeneracy assumption we also show that the uniform measure supported on any such polytope is a linear combination of uniform measures supported on simplices with vertices in S.
Forward citations
Cited by 1 Pith paper
-
Algebraic relations between moments of plane polygons
For an n-gon, all harmonic moments are rational functions of the first 2n-2 of them; adding anti-harmonic moments, the whole moment field is generated by the symmetric functions plus one area-like moment.
Discussion (0). Continue with ORCID to comment.