Proof step e-8dd7014bf6954b08

basis_map A013611 → concludes about basis_map_A013611 of Triangle of even numbered entries of odd 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

• Triangle of even numbered entries of odd numbered rows of Pascal's triangle A007318. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 2, "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 cf6bb673cd487ac267949e0f5226da424be682def90be52360e3f92aeb9836ce, 13,638 bytes (2,591 compressed); download JSON

Cited by

• n-14e292285dab27c9 (real_rooted)
• n-14e292285dab27c9 (one_signed_coefficients)
• n-14e292285dab27c9 (hadamard_kernel)
• n-14e292285dab27c9 (interlacing)