Combinatorics / CONCEPT
The first component and the layered tail
A nonempty permutation avoiding 312 and 54321 whose square avoids 132 consists of an indecomposable first component followed by decreasing components of length at most four.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES1
PROOF DEPTH6
DOCUMENT LINKS1
The last entry of an indecomposable component
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
- Counting Component Boundariesstructural-affinity · Closed
- Enumeration, generating series, and linear recurrencestructural-affinity · Closed
- Explicit families and first-entry boundsstructural-affinity · Closed
- First entry four and complete classificationstructural-affinity · Closed
- Indecomposability after Maximum Insertionstructural-affinity · Closed
- Permutation squares and the conjectured recurrencestructural-affinity · Closed
- The Archer-Bourne square recurrence fails at elevenstructural-affinity · Closed
- The corrected counting recurrencestructural-affinity · Closed
- The Fishburn Condition under Direct Sumstructural-affinity · Closed
- Unique Direct-Sum Componentsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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