Words / CONCEPT
A Counterexample Inside Vivion's Restricted Class
An explicit binary word answers Vivion's restricted converse question negatively: its second binomial complexity equals factor complexity at every length, its 1-binomial complexity is smaller at length two, and it is not 1-balanced.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES10
PROOF DEPTH1
DOCUMENT LINKS1
The restricted converse fails
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- AlternatingTwoDeletionCountstruth-dependency · Closed
- BinaryRunSupersequenceCountstruth-dependency · Closed
- CutoffCoefficientAlgebratruth-dependency · Closed
- ExactDeckCoretruth-dependency · Closed
- Finite Deletion-Channel Entropy Orderingtruth-dependency · Closed
- LyndonFactorizationtruth-dependency · Closed
- OverlapInfiltrationtruth-dependency · Closed
- PositivePairExactDeckAsymptoticstruth-dependency · Closed
- SinghviMaxInputEntropytruth-dependency · Closed
- TwoDeletionChannelEntropytruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- AlternatingTwoDeletionCountsstructural-affinity · Closed
- BinaryRunSupersequenceCountsstructural-affinity · Closed
- CutoffCoefficientAlgebrastructural-affinity · Closed
- ExactDeckCorestructural-affinity · Closed
- Finite Deletion-Channel Entropy Orderingstructural-affinity · Closed
- LyndonBracketAlgebrastructural-affinity · Closed
- LyndonFactorizationstructural-affinity · Closed
- LyndonOrderstructural-affinity · Closed
- LyndonStandardFactorizationstructural-affinity · Closed
- Natural Valuations Cannot Preserve Every Abelian Complexity Functionstructural-affinity · Closed
- OverlapInfiltrationstructural-affinity · Closed
- PositivePairExactDeckAsymptoticsstructural-affinity · Closed
- SinghviMaxInputEntropystructural-affinity · Closed
- The One-Sided Morse-Hedlund Theoremstructural-affinity · Closed
- Words: Morse Hedlund Conversestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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