Combinatorics / CONCEPT
The sharp product and its two positive spectral rays
Sharp product equality on labelled K2m determines the entire native spectrum.
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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH2
DOCUMENT LINKS0
The sharp bound, all equality restrictions and their full spectra
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- Connected nonnegative conductances on the original finite vertex setstructural-affinity · Closed
- Fixed resistance does not force an invariant Fiedler maximizerstructural-affinity · Closed
- Original tripartite conductances, trace compression and boundary rigiditystructural-affinity · Closed
- Strong cospectrality does not satisfy the general multiplicity boundstructural-affinity · Closed
- The fixed-resistance optimizer on the full labelled K2m familystructural-affinity · Closed
- The path-ends derivative does not minimize Kemeny's edge derivativestructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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