ConceptDynamics / CONCEPT
Archer-Bourne Decomposition
The permutations avoiding 312 and 321 are exactly the direct sums of cyclic rotations indexed by compositions, and the cube criterion gives the corresponding counting identity.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH1
DOCUMENT LINKS0
Positive rotation sums avoid both patterns
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- A Literal Negative Answer to Vatter's Question 4.3structural-affinity · Closed
- Actual fixed-cut factorizationstructural-affinity · Closed
- Actual minimum split and cardinal recurrencestructural-affinity · Closed
- Actual objects for the A398542 fixed-bottom conjecturestructural-affinity · Closed
- Classical avoidance and a proper cutstructural-affinity · Closed
- Greatest cuts and finite descent enumerationstructural-affinity · Closed
- No Largest Derangement Limit Below Onestructural-affinity · Closed
- Rotation-Sum Power Pattern Avoidancestructural-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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