Proof step e-69ce91caff12536e

basis_map A007318 → concludes about basis_map_A007318 of A Riordan array of coordination sequences. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• A Riordan array of coordination sequences. (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 c51108c236eb1fa4290086d8a6e0dee587f8c278fe6f1f9bbe411b247ef401ec, 14,011 bytes (2,695 compressed); download JSON

Cited by

• n-3c0665ea87e1dc8e (one_signed_coefficients)
• n-3c0665ea87e1dc8e (hadamard_kernel)
• n-3c0665ea87e1dc8e (interlacing)
• n-3c0665ea87e1dc8e (real_rooted)