Proof step e-20dcbad557ba463b

basis_map A013611 → concludes about basis_map_A013611 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": "A013611",
  "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 53a9abf74e85952adf31d097f531f79615997b15fa581b664d383003b24b47b0, 7,419 bytes (1,629 compressed); download JSON

Cited by

• n-b4b87865f0ed6035 (real_rooted)
• n-b4b87865f0ed6035 (one_signed_coefficients)
• n-b4b87865f0ed6035 (hadamard_kernel)