Combinatorics / CONCEPT
Degrees and the sharp count bound for legal words
Legal binary words have one neighbour per occupied position or flippable zero. The flippable-zero count plus twice the occupation count is at most n+1, with equality exactly for odd alternating words beginning and ending in one.
Closed
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES1
PROOF DEPTH2
DOCUMENT LINKS0
Degree equals additions plus removals
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 self-dual factorization of an irreducible thermal processstructural-affinity · Closed
- Binary kite-shaped quadratic formsstructural-affinity · Closed
- Constrained harmonic optimizationstructural-affinity · Closed
- Counting legal-word toggle edges by deletionstructural-affinity · Closed
- Even double paths with a nonempty loop setstructural-affinity · Closed
- Forbidden Neighbour Determinantstructural-affinity · Closed
- Forbidden-Neighbour Trace and Extensionstructural-affinity · Closed
- Legal chain integral and polar coordinatesstructural-affinity · Closed
- Legal chain moment and phase reductionstructural-affinity · Closed
- Positive Jacobi Cholesky Weightsstructural-affinity · Closed
- Quantum twins and neighbourhood separationstructural-affinity · Closed
- RRO Tail Linear-Length Setsstructural-affinity · Closed
- Sahbi's hypercube sub-quorum conjecturestructural-affinity · Closed
- Signed boundaries of legal-word toggle graphsstructural-affinity · Closed
- The Boolean hypercube and its edge countstructural-affinity · Closed
- The constraint polynomials of the two-photon Rabi model at and beyond the critical couplingstructural-affinity · Closed
- The Fibonacci Count of Zeckendorf-Admissible Wordsstructural-affinity · Closed
- The size distribution of nonadjacent supportsstructural-affinity · Closed
- Transport of native quadratic allocationsstructural-affinity · Closed
Documents & exposition
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