Erdős Problem #769
Prior state unknown→disproved
the conjectured lower bound is disproved; good bounds for c(n) remain open
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
geometry-topology / Discrete Geometry
Erdős Problem #769
For the least cutoff $c(n)$ after which every $k$ occurs as the number of homothetic cubes in a decomposition of the unit $n$-cube, is $c(n) \gg n^n$? The Lean proof shows $c(n) = o(n^n)$ along odd dimensions.
10Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts
Temporal state
Current frontier
No reconciled state yet.
Append-only history
Frontier timeline
Research memory
Claims and attempts
Scoped claims
For the least cutoff $c(n)$ after which every $k$ occurs as the number of homothetic cubes in a decomposition of the unit $n$-cube, is $c(n) \gg n^n$? The Lean proof shows $c(n) = o(n^n)$ along odd dimensions.
the conjectured lower bound is disproved; good bounds for c(n) remain open
Recorded attempts
Evidence graph
Connected research record
No public relationships recorded yet.