Analytic Spread via Linear Matroids

Stephen Landsittel, Eran Nevo

arXiv:2607.07458v1 Primary: math.AC Secondary: math.CO

Abstract

We give a systematic analysis of the analytic spread of the determinantal ideal $J_{G,H}$ arising from a pair of graphs $(G, H)$. We give sharp bounds for this analytic spread, and combinatorial conditions and obstructions for its maximality via a linear matroid. When $H$ is a single edge, $J_{G,H}$ is isomorphic to the binomial edge ideal $J_G$ and its analytic spread is shown to equal the rank of $G$ in Kalai's $2$-hyperconnectivity matroid.

Disclosure

“rvard, and the first author also thanks the Hebrew University of Jerusalem, for their support during this project. Both authors are partially supported by the Israel Science Foundation grant ISF-687/24. AI use statement. The authors used Gemini Pro during the revision stage of this paper for identifying typos and to double check calculations. All original results, proofs, and mathematical content predate the use of AI assistance. All AI-suggested edits were reviewed and approved by t”
PDF page 27

Classification: Computational experiments or data processing
Multiplier: 3
Verified: 2026-08-24T00:34:15.228Z

Structural counts

Pages 29 pdf

Theorems 6 source

Lemmas 11 source

Propositions 4 source

Corollaries 7 source

Definitions 6 source

Displayed equations 69 source

Bibliography entries 112 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file spread_arxiv_ver__1_.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.