Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
basis_map_A013611 of theta_plus_one of Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded in increa…
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-f7f6367d7d893706 · 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 e0015d7d315068e27dbb28c628ee0c42863bee76458c11aa731f2cd12668eb9c, 15,369 bytes (2,964 compressed); download
polytool replayed the certificate when the step was written.
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