Combinatorics / CONCEPT
The Archer-Bourne square recurrence fails at eleven
There are nine indecomposable permutations of length eleven avoiding 312 and 54321 whose squares avoid 132, which refutes the Archer-Bourne recurrence conjecture.
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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH8
DOCUMENT LINKS1
Completeness of maximum insertion
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Proof dependencyStructural affinityDocument link
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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
- The corrected counting recurrencestructural-affinity · Closed
- The first component and the layered tailstructural-affinity · Closed
- Unique Direct-Sum Componentsstructural-affinity · Closed
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