Proof step e-06cbef974e179f0a

basis_map A013610 → concludes about basis_map_A013610 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": "A013610",
  "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 dc094fd547bdb2aab468b1a241895d238a2d91f659a24adb90a5a1915a044282, 14,011 bytes (2,702 compressed); download JSON

Cited by

• n-23e2b6ed6bdac95d (real_rooted)
• n-23e2b6ed6bdac95d (one_signed_coefficients)
• n-23e2b6ed6bdac95d (hadamard_kernel)
• n-23e2b6ed6bdac95d (interlacing)