Proof step e-30bb9f6b8a15c298

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 4d8ad0f75823ccc7633f845d002ce9111b07b6441392bc9779def1759014b349, 14,011 bytes (2,703 compressed); download JSON

Cited by

• n-3dddab772a6867d2 (one_signed_coefficients)
• n-3dddab772a6867d2 (hadamard_kernel)
• n-3dddab772a6867d2 (interlacing)
• n-3dddab772a6867d2 (real_rooted)