Combinatorics / CONCEPT
Two-layer solid partitions with a second layer of size 3
The two-layer solid partitions whose first layer is a plane partition of n and whose second layer is a plane partition of 3 number 3(2 A000219(n) - A000990(n) - 2 A000041(n) + 1), with A000219 the plane partitions, A000990 the plane partitions with at most two rows and A000041 the partitions of n, as conjectured by W. Meeussen for OEIS A381265.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH2
DOCUMENT LINKS1
Proof of the conjecture
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
- First Sums of Decreasing Partitionsstructural-affinity · Closed
- Partitions with the fewest extensions are boxesstructural-affinity · Closed
- Strict First Sums and Gapfree Odd Partsstructural-affinity · Closed
- Threshold counts in overpartitionsstructural-affinity · Closed
- Zero-Prepended First Sums and Odd Partsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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