Combinatorics / CONCEPT
Skew-Merged Permutations Are Exactly Those With One or Two Placements
A permutation grid has exactly one or two complete rook placements if and only if its permutation is skew-merged.
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DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH8
DOCUMENT LINKS1
The skew-merged equivalence
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
- Boundary-Minimal Permutations and Their Placement Countsstructural-affinity · Closed
- Cuts for a Centerless Skew-Merged Permutationstructural-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
- Split Graphs and Forbidden Permutation Patternsstructural-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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