Metadata
bibkey: spezia2019a330700
authors: Stefano Spezia
year: 2019
title: OEIS A330700, second exterior-trace conjecture
doi: null
url: https://oeis.org/A330700
claim: "For k > 2, the trace of the k-th exterior power of M(n) is equal to zero."
strata_touched:
- D5/S3/Quantum/Matrix/SpeziaPerimeterHigherExteriorTraces
license: citation-only
triage: anchor
Verified locator
Source: https://oeis.org/A330700
OEIS A330700, COMMENTS, revision 23, second line of the Conjectures block (unpaginated):
For k > 2, the trace of the k-th exterior power of M(n) is equal to zero.
The matrix is specified in the preceding line of the same block and in OEIS A330287, COMMENTS, revision 31 (unpaginated):
The matrix M(n) is defined as M[i,j,n] = ij if i < 3 or j < 3 and M[i,j,n] = 2(i + j) - 4 otherwise.
The row and column indices start at one, as in the displayed A330287 example
M(3) with rows (1,2,3), (2,4,6), (3,6,8). This is the principal perimeter
matrix of OEIS A319840. In Lean, indices are
Fin n, source indices are i.val + 1 and j.val + 1, and the integer
entries are interpreted in ℂ. The claim ranges over every positive natural
matrix order and every natural exterior order greater than two. The existing
compoundMatrix represents the exterior map in its ordered-subset basis;
Matrix.trace is its trace, including the empty-basis case k > n.
This source is an OEIS entry and has no identified arXiv version or DOI. The scalar-sequence assertion about the absolute second exterior trace is a separate conjecture. OEIS material is subject to the OEIS End-User License.