Proof step e-159425c642d412bb

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: T(n,k) = C(n+3,3) * C(n,k), 0 <= k <= n. 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) = C(n+3,3) * C(n,k), 0 <= k <= n. (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 5c270456d0b1ec88f5cdc6f7684b998bdb6d47cc4bb79f9297d9243f7c0c3ba6, 13,199 bytes (2,507 compressed); download JSON

Cited by

• n-77621b0cfa8249dd (real_rooted)
• n-77621b0cfa8249dd (one_signed_coefficients)
• n-77621b0cfa8249dd (hadamard_kernel)
• n-77621b0cfa8249dd (interlacing)