Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013611

Concludes

Premises

Triangle read by rows: T(n,k) = ((n+1)(n+2)/2) * binomial(n,k) (0 <= k <= n).
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-89b0bff9927fbc5c · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Claims

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

Certificate

basis_map, SHA-256 6ce1390a12ddc046840c9b0472db8b699aae0eddc33e3322e46d844c88c82e3a, 12,507 bytes (2,193 compressed); download

polytool replayed the certificate when the step was written.

Cited by