Proof step e-0f3734a094503340

basis_map A013609 → concludes about basis_map_A013609 of Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n). (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 a1a42c35349e9c9e96e62bc4453110aa2fbd34f40c6d11f1007095f4a5e0bb08, 7,419 bytes (1,626 compressed); download JSON

Cited by

• n-1a3a6cbc48d40fe3 (real_rooted)
• n-1a3a6cbc48d40fe3 (one_signed_coefficients)
• n-1a3a6cbc48d40fe3 (hadamard_kernel)