Proof step e-d7c15f9b4df77eea

basis_map A013610 → concludes about basis_map_A013610 of Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments. (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 2d5dafe342aebb37079612ee0bf523daba977d6f04a9abaae7e7240e08e43bd9, 14,013 bytes (2,711 compressed); download JSON

Cited by

• n-3f3ffed71cecca6c (interlacing)
• n-3f3ffed71cecca6c (real_rooted)
• n-3f3ffed71cecca6c (one_signed_coefficients)
• n-3f3ffed71cecca6c (hadamard_kernel)