Combinatorics / CONCEPT
Every Natural Rook-Placement Count Occurs
An alternating five-column family realizes every positive count, and a three-by-three grid realizes zero.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH1
DOCUMENT LINKS1
Horizontal row intervals
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 Permutation Grid with 155 Rook Placementsstructural-affinity · Closed
- Boundary-Minimal Permutations and Their Placement Countsstructural-affinity · Closed
- Crossword Grids and Rook 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
- Words and Symmetries of Permutation Gridsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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