Combinatorics / CONCEPT
Intervals and simplicity in the terminal families
For n at least four, R(n) is a permutation of size n in C ending in its minimum. Its proper nontrivial intervals are exactly the prefix of length n minus one with values from two through n and, when n is even, the second and third entries with values n minus one and n. Moreover, Y(n+1) is a simple permutation of size n + 1 in C.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES1
PROOF DEPTH6
DOCUMENT LINKS1
Intervals and simplicity in the terminal families
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 bijection to second-position minimastructural-affinity · Closed
- Classification of a terminal crossing gapstructural-affinity · Closed
- Deleting a minimum in the second positionstructural-affinity · Closed
- Inserting a minimum in an early gapstructural-affinity · Closed
- Prepending a new second-smallest entrystructural-affinity · Closed
- Simplicity after prepending twostructural-affinity · Closed
- The five cases for a third-position minimumstructural-affinity · Closed
- The reverse third-position constructionstructural-affinity · Closed
- The unique proper interval of an odd extrastructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
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