Combinatorics / CONCEPT
Disjoint-union uniqueness and intersecting links
Let H be a finite family of subsets of an arbitrary finite vertex type with n vertices. The definitions apply to every such H; three-uniformity, DUF, and the cap are assumptions only where stated. Unordered pairs range over the whole ground set, so absent pairs are included. The pair extension relation is directed; a common link is obtained by transposing that relation.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES4
PROOF DEPTH0
DOCUMENT LINKS1
Star or triangle
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
None recorded in this release.
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Exact stars at a marked packetstructural-affinity · Closed
- Local graphs and owned triangle rowsstructural-affinity · Closed
- Local graphs and reciprocal double countingstructural-affinity · Closed
- Mixed vertices and actual triangle packetsstructural-affinity · Closed
- Ownership at a marked exchangestructural-affinity · Closed
- Three-color reciprocal inequalitystructural-affinity · Closed
- Two incidence counts and the codegree-four boundstructural-affinity · Closed
- Unordered wedges and four-edge common linksstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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