Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013609

Concludes

Premises

Triangle of central factorial numbers |t(2n,2n-2k)| read by rows.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-031a48225080e193 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "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 66ee81c0c8fa7be1713102d4c913d6f20690f5e5e0aa4e5454965cfef0eb7ea3, 10,294 bytes (2,288 compressed); download

polytool replayed the certificate when the step was written.

Cited by