Proof step e-597992a3fe650259

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 79995d33004f9dd3ecb316c5f7a1853ee259aca00f4eb7c5519e397603649bfe, 14,059 bytes (2,687 compressed); download JSON

Cited by

• n-5bdff9de6e987505 (real_rooted)
• n-5bdff9de6e987505 (one_signed_coefficients)
• n-5bdff9de6e987505 (hadamard_kernel)
• n-5bdff9de6e987505 (interlacing)