DefinitionDefinition: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-26

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

$L$ -intersecting families

Definition

Fix $n \in N$ and let $L \subseteq N$ be finite. A family $F$ of subsets of $[n]$ is $L$ -intersecting when

$∣ A \cap B ∣ \in L for every distinct A, B \in F .$

No condition is imposed on the sizes $∣ A ∣$ of the individual sets.

Remarks

The case $L = {t}$ is the constant-intersection situation of Fisher's inequality. The Frankl-Wilson theorem treats several allowed intersection sizes at once.

Depends on

Used by

Dependency tree · two levels

20 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

L. Babai and P. Frankl, Linear Algebra Methods in Combinatorics, §4.3 (standard reference, not scraped)
J. Matousek, Thirty-three Miniatures, Miniature 17 (standard reference, not scraped)

LL-intersecting families