Proof step e-489412f9b4065fef

basis_map A013609 → concludes about basis_map_A013609 of Riordan array (1/((1-x)(1-3x)),x/((1-x)(1-3x))). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Riordan array (1/((1-x)(1-3x)),x/((1-x)(1-3x))). (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 87a60c4e6e63994d22460b911e74d5d879b7a8c81ce8bad8c23e0cea39dc5f6d, 13,345 bytes (2,523 compressed); download JSON

Cited by

• n-817434b322e3be5b (real_rooted)
• n-817434b322e3be5b (one_signed_coefficients)
• n-817434b322e3be5b (hadamard_kernel)
• n-817434b322e3be5b (interlacing)