Proof step e-0e122e2df114c72b

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows, Stirling cycle numbers of order 3, T(n,n) = 1, T(n,k) = 0 if k<0 or k>n, otherwise T(n,k) = T(n-1,k-1)+(n-1)^3*T(n-… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle read by rows, Stirling cycle numbers of order 3, T(n,n) = 1, T(n,k) = 0 if k<0 or k>n, otherwise T(n,k) = T(n-1,k-1)+(n-1)^3*T(n-1… (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 a8b964d12efba7a2ceb462567ae45bd4a41edb5d2cbbe6f7f3fcdc3d195e6a0e, 7,517 bytes (1,624 compressed); download JSON

Cited by

• n-b096a5459ca672a4 (real_rooted)
• n-b096a5459ca672a4 (one_signed_coefficients)
• n-b096a5459ca672a4 (hadamard_kernel)