FiniteGroups / CONCEPT
First-return defect for the same actual quotients
The first signed word-return defect separates two actual markings of one finite quotient group.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH8
DOCUMENT LINKS0
Equal short signed word fibers and the first two extra returns
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 missing square point forces a smaller Lee coverstructural-affinity · Closed
- Abstract finite noncyclic upper boundsstructural-affinity · Closed
- Exact endpoint count for signed coordinate wordsstructural-affinity · Closed
- Exact first even return band for the two lattice quotientsstructural-affinity · Closed
- Exact first reversal and the complete final pre-wrap bandstructural-affinity · Closed
- Exact growth and diameter of asymmetric lattice quotientsstructural-affinity · Closed
- Exact growth from finite rank-one fibersstructural-affinity · Closed
- Exact returns at the first odd wrapstructural-affinity · Closed
- From actual quotient return words to simple Cayley graph momentsstructural-affinity · Closed
- One group and exact growth gaps for all odd square displacementsstructural-affinity · Closed
- Rigidity from adjacent columns and quotient indexstructural-affinity · Closed
- Same group and diameter, different growthstructural-affinity · Closed
- The Bajnok–Beatty sharp maximum for radius at least threestructural-affinity · Closed
- The first characteristic coefficient separating the actual Cayley graphsstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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