Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
basis_map_A013611 of basis_map_A007318 of Triangle read by rows. T(n, k) = RisingFactorial(n + 1, n) / (k! * (n - k)!).
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-bd03fe5772dbb363 · 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"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 a2f2cda3c5f827c39ba73ddbd5c6e88186a60c2fc109cf50ff30bdfeb43b3a71, 10,528 bytes (2,334 compressed); download
polytool replayed the certificate when the step was written.
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