The integrality gap of weighted $k$ -matroid intersection

Partial on the headline conjecture, complete on a named part of another. For weighted $k$ -matroid intersection the integrality gap is at most $k - 1 + 1/k$ , improving the previous general bound of $k$ but not reaching the conjectured $k-1$ . For weighted $p$ -matchoids the gap is at most $p - 1 + 1/p$ , with a deterministic LP-relative algorithm achieving the same factor; the paper states that this resolves the $p$ -matchoid part of Lee, Sviridenko and Vondrák's Conjecture 1, and projective planes of order $p-1$ give tight instances whenever one exists.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 18, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The integrality gap of weighted $k$-matroid intersection · Matroid intersection integrality gap

Confidence: Not scored

Registry verification: unreviewed · preprint · partial

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Attribution

VibeMathed
registry · event recorded by

GPT-5.6 Sol
model · ai model contributor · OpenAI

Yu Cong
human · human collaborator

Yajie Zhao
human · human collaborator

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VibeMathed record: The integrality gap of weighted $k$ -matroid intersection

specialist registry · passed

Checked here on 27 September 2026 against arXiv:2609.21477, posted 18 September. The abstract and introduction were read: the $k$ -matroid bound improves from $k$ to $k-1+1/k$ , short of the conjectured $k-1$ , and the $p$ -matchoid result attains $p-1+1/p$ with a deterministic LP-relative algorithm, which the paper says resolves the $p$ -matchoid part of Lee, Sviridenko and Vondrák's Conjecture 1, projective planes of order $p-1$ giving tight instances where one exists. The AI Disclosure is one sentence and is quoted in the AI role field. The mathematics was not checked here; nine days old, no referee, no formalisation.

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The integrality gap of weighted $k$ -matroid intersection

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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This event attributed to Yajie Zhao

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The integrality gap of weighted $k$ -matroid intersection evidence for this event

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This event attributed to Yu Cong

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