Proof step e-5d127e92ec7ea44a

basis_map A013609 → concludes about basis_map_A013609 of Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n. (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 5cfc718a57f14adc527c6feb7a4462fa010d2f2d0d7fb0a180c2e4af36fb49d3, 7,412 bytes (1,618 compressed); download JSON

Cited by

• n-306852163f00b660 (real_rooted)
• n-306852163f00b660 (one_signed_coefficients)
• n-306852163f00b660 (hadamard_kernel)