Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
basis_map_A013609 of Irregular triangle read by rows: T(n,k) = binomial(n-k, k), n >= 0, 0 <= k <= floor(n/2); or, coefficients of (one version of) Fibonacci p…
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-f864d29127dce965 · 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 158d2e52ccebf9ed8c2e4ef293b3c131940bf8d90b4893e3538c4042cf868e42, 10,829 bytes (2,449 compressed); download
polytool replayed the certificate when the step was written.
Cited by