Proof step e-fb7c8bbf92df84a6

basis_map A013609 → concludes about basis_map_A013609 of Triangle of coefficients in expansion of (1+x)*(1+3x)*(1+5x)*(1+7x)*...*(1+(2n-1)x). 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 in expansion of (1+x)*(1+3x)*(1+5x)*(1+7x)*...*(1+(2n-1)x). (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 8fa5a2804f4dbf1e4d8f5fe677cc47979b87473fe1286a787d6acea0538ced77, 10,164 bytes (2,290 compressed); download JSON

Cited by

• n-a6229b8a5ae7f968 (real_rooted)
• n-a6229b8a5ae7f968 (one_signed_coefficients)
• n-a6229b8a5ae7f968 (hadamard_kernel)
• n-a6229b8a5ae7f968 (interlacing)