Proof step e-b9afd27e557143a1

basis_map A007318 → concludes about basis_map_A007318 of Pascal-(1,8,1) array. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Pascal-(1,8,1) array. (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 14435802203216650f978ba512dedaffb8f3929fbe9c94dfc3f8661c45dc4316, 14,011 bytes (2,699 compressed); download JSON

Cited by

• n-b645b69a268eebb3 (real_rooted)
• n-b645b69a268eebb3 (one_signed_coefficients)
• n-b645b69a268eebb3 (hadamard_kernel)
• n-b645b69a268eebb3 (interlacing)