Pith. sign in

REVIEW 1 cited by

Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix

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

arxiv 2312.12247 v2 pith:LUQO3FAV submitted 2023-12-19 math.AC math.AG

classification math.ACmath.AG
keywords timesidealpermanentsmatrixbernstein-gelfand-gelfandgenericworkarising
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We describe the minimal free resolution of the ideal of $2 \times 2$ subpermanents of a $2 \times n$ generic matrix $M$. In contrast to the case of $2 \times 2$ determinants, the $2 \times 2$ permanents define an ideal which is neither prime nor Cohen-Macaulay. We combine work of Laubenbacher-Swanson on the Gr\"obner basis of an ideal of $2 \times 2$ permanents of a generic matrix with our previous work connecting the initial ideal of $2 \times 2$ permanents to a simplicial complex. The main technical tool is a spectral sequence arising from the Bernstein-Gelfand-Gelfand correspondence.

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

  1. Equivariant Syzygies of the Ideal of 2 x 2 Permanents of a 2 x n Matrix

    math.AC 2025-02 conditional novelty 7.0 of 10

    The syzygies of the ideal of 2x2 permanents of a 2xn matrix are described as explicit representations of the symmetric group and torus actions.

Pith tools