The Cayley-Menger determinant is irreducible for $n\geq 3$

Carlos D'Andrea; Martin Sombra

The Cayley-Menger determinant is irreducible for $n\geq 3$

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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

arxiv math/0406359 v1 pith:NPKEX4GZ submitted 2004-06-18 math.AC math.MG

Carlos D'Andrea , Martin Sombra This is my paper · ORCID

classification math.ACmath.MG

keywords cayley-mengerdeterminantirreducibleabsolutelyassociatedconstructionsdimensionalgeometric

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

We prove that the Cayley-Menger determinant of an $n$-dimensional simplex is an absolutely irreducible polynomial for $n\geq3.$ We also study the irreducibility of polynomials associated to related geometric constructions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Higher-Spin Correlators in dS
hep-th 2026-08 accept novelty 8.0 of 10

The five-point de Sitter higher-spin correlator is shown to be a spurious-singularity-free rational function organized by graph-theoretic orbits of the complete graph K5.

Pith tools