Combinatorics / CONCEPT
The two value regions below a second-position maximum
For a permutation of size at least four with maximum second, consider its suffix after the first two entries. Require that values above the first entry decrease and that no value below the first entry has both a smaller and a larger such value later. These two conditions imply membership in C, and every simple member of C with maximum second satisfies them.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH2
DOCUMENT LINKS1
The two value regions below a second-position maximum
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 cut into decreasing chainsstructural-affinity · Closed
- An ascent in the second inflated blockstructural-affinity · Closed
- An exhausted lower chainstructural-affinity · Closed
- Avoidance under ordinary continuationstructural-affinity · Closed
- Inserting a minimum in an early gapstructural-affinity · Closed
- Intervals when the maximum is secondstructural-affinity · Closed
- Ordinary continuationstructural-affinity · Closed
- Simplicity of the parallel familystructural-affinity · Closed
- The alternating prefix before the minimumstructural-affinity · Closed
- The Fibonacci enumeration assertionstructural-affinity · Closed
- The first and third values before a late minimumstructural-affinity · Closed
- The unique proper interval of an odd extrastructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
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