Combinatorics / CONCEPT
Italian dominating functions on cycles
The total number of Italian dominating functions on the labelled cycle C_n, for n at least three, satisfies a constant-coefficient recurrence of order five. Its first five values are 23, 60, 167, 467 and 1297. A bijection with closed sequences in a nine-state transfer matrix identifies the count with a power trace; a five-state factorization then supplies the recurrence.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES2
PROOF DEPTH0
DOCUMENT LINKS1
A complete order-five recurrence
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
None recorded in this release.
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- A 23-edge coupling realizes the ten-mode Fourier transformstructural-affinity · Closed
- Actual membership words and cyclic boundariesstructural-affinity · Closed
- Counting based labelled closed runsstructural-affinity · Closed
- CZX coordinate averagingstructural-affinity · Closed
- CZX parent Lindbladian steady statestructural-affinity · Closed
- CZX parent-Lindbladian window channelstructural-affinity · Closed
- Enumeration prerequisites for the original identitystructural-affinity · Closed
- The Andrasfai forbidden languagestructural-affinity · Closed
- The corrected transfer-trace seriesstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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