Proof step

Geometric basis map (elementary)

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

Concludes

Premises

Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-e5d5647736973415 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "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 bcef6ec1e6862a436e2f0d8b5ae2547c3629438b93f1122a4391ed06dd783e2e, 10,787 bytes (2,381 compressed); download

polytool replayed the certificate when the step was written.

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