Proof step e-5acf27e3646b3b0e

basis_map A013610 → concludes about basis_map_A013610 of Triangle T(n, k) is coefficient of z^n*w^k in 1/(1 - 2*z - 2*w - 2*z*w) read by rows in order 00, 10, 01, 20, 11, 02, ... JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle T(n, k) is coefficient of z^n*w^k in 1/(1 - 2*z - 2*w - 2*z*w) read by rows in order 00, 10, 01, 20, 11, 02, ... (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 7a5b2b14706f8764e1355d48e09b8716f35d86ba913a7726d720d988f49bea37, 14,052 bytes (2,700 compressed); download JSON

Cited by

• n-e6d483569f3966cd (real_rooted)
• n-e6d483569f3966cd (one_signed_coefficients)
• n-e6d483569f3966cd (hadamard_kernel)
• n-e6d483569f3966cd (interlacing)