Proof step e-7d8fca0f88bff382

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1). (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 3ea76e0f9bd9cbe47b92040523070af27add0b8d5096fcc481279e3e2927b65c, 13,345 bytes (2,522 compressed); download JSON

Cited by

• n-02f1a3354aa99430 (real_rooted)
• n-02f1a3354aa99430 (one_signed_coefficients)
• n-02f1a3354aa99430 (hadamard_kernel)
• n-02f1a3354aa99430 (interlacing)