Proof step e-24d6e61d1fff2e02

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 e0ce1eefbe5d60c78ec1d07c946879edc9ec6ad4aa509e332b4dcf6ba70399bc, 13,634 bytes (2,579 compressed); download JSON

Cited by

• n-3d55772447340781 (real_rooted)
• n-3d55772447340781 (one_signed_coefficients)
• n-3d55772447340781 (hadamard_kernel)
• n-3d55772447340781 (interlacing)