Combinatorics / CONCEPT
Split Graphs and Forbidden Permutation Patterns
A graph without the three forbidden induced configurations splits into a clique and an independent set, and skew-merged permutations are exactly the 2143- and 3412-avoiders.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH3
DOCUMENT LINKS1
A clique and an independent set
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
- A Permutation Grid with 155 Rook Placementsstructural-affinity · Closed
- Boundary-Minimal Permutations and Their Placement Countsstructural-affinity · Closed
- Crossword Grids and Rook Placementsstructural-affinity · Closed
- Cuts for a Centerless Skew-Merged Permutationstructural-affinity · Closed
- Every Natural Rook-Placement Count Occursstructural-affinity · Closed
- Existence and Uniqueness of Complete Placementsstructural-affinity · Closed
- Placement Counts Under Extreme Insertionsstructural-affinity · Closed
- Skew-Merged Permutations and Rook Placementsstructural-affinity · Closed
- Skew-Merged Permutations Are Exactly Those With One or Two Placementsstructural-affinity · Closed
- The Forward Implicationstructural-affinity · Closed
- Words and Symmetries of Permutation Gridsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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