Combinatorics / CONCEPT
Direct prefix partitions and their two fan moments
A binary word traces positive unit steps in one oriented plane. Signed triangle sums give area and centered first moments, including paths of zero signed area. The reverse list of horizontal prefix counts at vertical letters is a padded decreasing partition. Its row and conjugate column squares determine the two centered moments of the same word at its direct area count.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH8
DOCUMENT LINKS0
Appending a supplied letter
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
- Ancestor Area and Intrinsic Depth Instabilitystructural-affinity · Closed
- Binary Parikh matrices and step-two Chen coordinatesstructural-affinity · Closed
- Golden factors through Parikh and Magnus coordinatesstructural-affinity · Closed
- Magnus center, reversal and the exact length-parity boundarystructural-affinity · Closed
- Projection Commutator Identitystructural-affinity · Closed
- Sharp Entrance Ratios on Entire Actual Geometry Fibersstructural-affinity · Closed
- Step-Two Chronological Logarithmstructural-affinity · Closed
- Step-Two Chronological Signaturestructural-affinity · Closed
- Word reconstruction and the full joint imagestructural-affinity · Closed
Documents & exposition
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Other authored & advisory relationships
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LIBRARY / RELEASE VERSIONS
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