Proof step e-61d2480a3633cd97

basis_map A013611 → concludes about basis_map_A013611 of One half of odd-numbered entries of even-numbered rows of Pascal's triangle A007318. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• One half of odd-numbered entries of even-numbered rows of Pascal's triangle A007318. (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 28cb6f5b5a8855e0a8fd3e52eadcde6bdc0ab314cb9736e4bec34cbeea3c6978, 13,636 bytes (2,584 compressed); download JSON

Cited by

• n-55371dcfaf771579 (real_rooted)
• n-55371dcfaf771579 (one_signed_coefficients)
• n-55371dcfaf771579 (hadamard_kernel)
• n-55371dcfaf771579 (interlacing)