Proof step e-3581c2f82a666ba6

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows: T(n,k) = (-1)^(n+k)*Sum_{j=1..k} s(n,j), where s(n,j) are the signed Stirling numbers of the first kind (n >= 2; 1 … JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) = (-1)^(n+k)*Sum_{j=1..k} s(n,j), where s(n,j) are the signed Stirling numbers of the first kind (n >= 2; 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 a87dfe7a895a97c24f21c77bcc5f5ba9665d22809947f1dfa82684b06bb53e91, 7,400 bytes (1,618 compressed); download JSON

Cited by

• n-fb9493e648020cca (real_rooted)
• n-fb9493e648020cca (one_signed_coefficients)
• n-fb9493e648020cca (hadamard_kernel)