Proof step e-bf3b7a758db4c427

basis_map A013610 → concludes about basis_map_A013610 of Triangle read by rows, s_4(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": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle read by rows, s_4(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 a360f59d6bfff5e3f8fff8992669a5053962ec72d1cb41662379963e0c8215d1, 7,412 bytes (1,620 compressed); download JSON

Cited by

• n-a06f8ee83f308dcc (real_rooted)
• n-a06f8ee83f308dcc (one_signed_coefficients)
• n-a06f8ee83f308dcc (hadamard_kernel)