Combinatorics / CONCEPT
The generating function for matchings avoiding 123, 132 and 213
The Catalan-Fibonacci series gives the generating function of all perfect matchings avoiding 123, 132 and 213.
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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH8
DOCUMENT LINKS1
The perfect-matching enumeration
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 bijection between avoiding matchings and accepted wordsstructural-affinity · Closed
- Avoiding matchings yield accepted scan wordsstructural-affinity · Closed
- Catalan-Fibonacci enumeration above the boundarystructural-affinity · Closed
- Constructing a matching from every accepted scanstructural-affinity · Closed
- Decoding accepted action words into perfect matchingsstructural-affinity · Closed
- Generating functions of accepted suffixesstructural-affinity · Closed
- Normalized bases and pending openingsstructural-affinity · Closed
- The future order of arcs avoiding P13structural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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