Proof step e-38bf0b24f025cc0b

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: T(1,1)=1,T(2,1)=1,T(2,2)=3, T(k-1,r-1)+T(k-1,r)+T(k-2,r-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(1,1)=1,T(2,1)=1,T(2,2)=3, T(k-1,r-1)+T(k-1,r)+T(k-2,r-1). (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 261bd1cbe6f1a7bc197b3afccd58a1bcaaeef893c81c39b167c82c11cce0e666, 14,013 bytes (2,702 compressed); download JSON

Cited by

• n-baf4dd53b457b011 (real_rooted)
• n-baf4dd53b457b011 (one_signed_coefficients)
• n-baf4dd53b457b011 (hadamard_kernel)
• n-baf4dd53b457b011 (interlacing)