Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
basis_map_A013609 of basis_map_A013610 of Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-8548c09c5947adcc · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013609",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 2,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 c8db17ce6cea151250d5f6d3365c3d0657e1fbd2b0339f39e061e9fd7acf155f, 13,480 bytes (2,561 compressed); download
polytool replayed the certificate when the step was written.
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