Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A007318

Concludes

Triangle read by rows: T(n,k) = binomial(k,n-k).

Premises

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

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-c11db06c1685e2a1 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "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 d836c1c50b7055815d62f23ea706c0c257165e12efd92e494808dab2aec0e797, 14,335 bytes (2,753 compressed); download

polytool replayed the certificate when the step was written.

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