Combinatorics / CONCEPT
An ordered scan characterizes pattern avoidance
Pattern avoidance is equivalent to closing the oldest or second-oldest open arc with a conditional constraint on the next closure.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH1
DOCUMENT LINKS1
Equivalence of avoidance and the scan rule
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
- Avoiding matchings yield accepted scan wordsstructural-affinity · Closed
- Constructing a matching from every accepted scanstructural-affinity · Closed
- Decoding accepted action words into perfect matchingsstructural-affinity · Closed
- Encoding matchings by labeled scan actionsstructural-affinity · Closed
- Normalized bases and pending openingsstructural-affinity · Closed
- Perfect matchings and the Catalan-Fibonacci generating functionstructural-affinity · Closed
- The future order of arcs avoiding P13structural-affinity · Closed
- Transporting total orders through queue deletionstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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