Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A038279

Concludes

Riordan array (1, 3+3x).

Premises

basis-map coefficients of Riordan array (1, 3+3x).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 8]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-d2fa4e847d2ea7db · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A038279",
  "operation": "basis_map"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 f6301fe2d7d582338e03429f50d9434d05617cefd8ced495bf834686887f5e3c, 14,426 bytes (2,797 compressed); download

polytool replayed the certificate when the step was written.

Cited by