Combinatorics / CONCEPT
The Catalan functional on paths
The integer alternating Catalan functional on actual independent sets is nonnegative on every finite path at every parameter at least its number of vertices.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH1
DOCUMENT LINKS0
Every legal parameter
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
- 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 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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