Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
basis_map_A013610 of Triangle read by rows: T(n,k) is the number of Schroeder paths of semilength n containing exactly k peaks but no peaks at level one (n >= …
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-125d456539fb62ba · 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 f3f723692cef6c224df65df44dfb23efa23343cd6054c4818ac263e6616bb0e4, 14,117 bytes (2,661 compressed); download
polytool replayed the certificate when the step was written.
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