Proof step e-7348ffa4b4bbc682

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows: T(n, k) = binomial(2n, 2k). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n, k) = binomial(2n, 2k). (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 c00104b0b3dac58838c0be2025c9e6cf6bf8a1d882ddd4eef311382441eb7717, 13,634 bytes (2,583 compressed); download JSON

Cited by

• n-c1716beb5dbd6d37 (real_rooted)
• n-c1716beb5dbd6d37 (one_signed_coefficients)
• n-c1716beb5dbd6d37 (hadamard_kernel)
• n-c1716beb5dbd6d37 (interlacing)