Proof step e-6ce7f219250b8b1f

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows, s_3(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle read by rows, s_3(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0. (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 5137f8caa79b6765d5094d939ed0203779b2a6f5f798db9997efd94b5ddb6be8, 7,412 bytes (1,620 compressed); download JSON

Cited by

• n-7ba399ade8b53e3c (real_rooted)
• n-7ba399ade8b53e3c (one_signed_coefficients)
• n-7ba399ade8b53e3c (hadamard_kernel)