Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013610

Concludes

Premises

Triangle for first differences of Catalan numbers.
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-af0c4734b9f5f6e6 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Claims

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

Certificate

basis_map, SHA-256 f0b27f77895f43ab76e4ebbe4c33427e3a267bab0f9c6f7532caa59b89cdc56d, 12,893 bytes (2,247 compressed); download

polytool replayed the certificate when the step was written.

Cited by