StatisticalMechanics / CONCEPT
A counterexample to the multivariate hard-core occupancy bound
The three-vertex star with fugacities (15,2,2) has expected independent-set size 9/8, below the proposed degree-sequence lower bound 259/230.
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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH1
DOCUMENT LINKS1
The three-vertex star refutes the bound
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
- Actual real partition messagesstructural-affinity · Closed
- Dissipative free-fermion roots in the upper half-planestructural-affinity · Closed
- GibbsOccupationstructural-affinity · Closed
- Independent-set partition and deletionstructural-affinity · Closed
- OccupationMomentsstructural-affinity · Closed
- Ordered partition recursionstructural-affinity · Closed
- PartitionRelabelingstructural-affinity · Closed
- The Catalan functional on finite linear forestsstructural-affinity · Closed
- The Catalan functional on pathsstructural-affinity · Closed
- The Triangular Prism Refutes Pandey's Parity Conjecturestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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