Combinatorics / CONCEPT
Cyclic Latin Eulerian Numbers Are Not Fully Symmetric
The column-ascent counts of cyclic Latin squares change only when an endpoint symbol wraps, which refutes full permutation symmetry of the ascent vector.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH1
DOCUMENT LINKS1
One-column shift identity
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
- Explicit Permutation Statisticsstructural-affinity · Closed
- Interior Multiples of the Latin Eulerian Totalstructural-affinity · Closed
- Latin Squares and Column Ascentsstructural-affinity · Closed
- Latinness of the literal H familystructural-affinity · Closed
- Near-Line Avoidance on the Three-Dimensional Boardstructural-affinity · Closed
- Residue Comparisons After Swapping Zero and Onestructural-affinity · Closed
- Row Counting and Row Reversalstructural-affinity · Closed
- The distinguished-entry obstructionstructural-affinity · Closed
- The Shifted-Square Ascent Formulastructural-affinity · Closed
- Three transversals of the H familystructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance