Combinatorics / CONCEPT
The Fibonacci enumeration assertion
The assertion is that the numbers of simple permutations in C of sizes zero, one and two are respectively one, one and two, and that for every n at least three the number is F_(2n-5) minus the remainder of n on division by two. The Fibonacci sequence has F_0 = 0 and F_1 = 1.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES6
PROOF DEPTH1
DOCUMENT LINKS1
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A cut into decreasing chainstruth-dependency · Closed
- An ascent in the second inflated blocktruth-dependency · Closed
- Inserting a minimum in an early gaptruth-dependency · Closed
- Ordinary continuationtruth-dependency · Closed
- The first and third values before a late minimumtruth-dependency · Closed
- The two value regions below a second-position maximumtruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A cut into decreasing chainsstructural-affinity · Closed
- An ascent in the second inflated blockstructural-affinity · Closed
- Arrow Patterns and Their Avoidance Classesstructural-affinity · Closed
- Cyclic Pattern Avoidancestructural-affinity · Closed
- Fixed Points and the Two Avoidance Conditionsstructural-affinity · Closed
- Inserting a minimum in an early gapstructural-affinity · Closed
- Ordinary continuationstructural-affinity · Closed
- The first and third values before a late minimumstructural-affinity · Closed
- The two value regions below a second-position maximumstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance