Combinatorics / CONCEPT
The Catalan functional on finite linear forests
The alternating Catalan sum over all actual independent subsets of every finite acyclic graph of maximum degree two is nonnegative at every parameter at least its full vertex count.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH2
DOCUMENT LINKS0
All vertices and all legal parameters
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- A counterexample to the multivariate hard-core occupancy boundstructural-affinity · Closed
- Actual real partition messagesstructural-affinity · Closed
- Concentrating two paths on the original bipartitionstructural-affinity · Closed
- Dissipative free-fermion roots in the upper half-planestructural-affinity · Closed
- GibbsOccupationstructural-affinity · Closed
- OccupationMomentsstructural-affinity · Closed
- Ordered partition recursionstructural-affinity · Closed
- PartitionRelabelingstructural-affinity · Closed
- The Catalan functional on pathsstructural-affinity · Closed
- The Triangular Prism Refutes Pandey's Parity Conjecturestructural-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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