Proof step e-42bb566932c0b2ac

basis_map A013609 → concludes about basis_map_A013609 of Triangle of coefficients of (x+1)*(x+3)*(x+6)*...*(x+n(n+1)/2). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle of coefficients of (x+1)*(x+3)*(x+6)*...*(x+n(n+1)/2). (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 e943630aada5cbab67331e15e767d11a5fef1c06aa641a894fb486c90efd492d, 10,242 bytes (2,303 compressed); download JSON

Cited by

• n-623036dc25b33b8c (one_signed_coefficients)
• n-623036dc25b33b8c (hadamard_kernel)
• n-623036dc25b33b8c (interlacing)
• n-623036dc25b33b8c (real_rooted)