Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
basis_map_A013610 of basis_map_A007318 of Triangle T(n, k) read by rows: T(n, k) = Sum_{j=0..n} binomial(j, n-k) * |Stirling1(n, n-j)|.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-0ce9da52d64bbd3b · 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"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 af18c4f6ea6e77eaf3cff23d95e28262638e47e23da91e536d5dab7f5bc5c6aa, 10,257 bytes (2,291 compressed); download
polytool replayed the certificate when the step was written.
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