Proof step

Geometric basis map (elementary)

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

Concludes

Premises

shift_x_plus_one of Number triangle T(n,k)=C(n,k)C(2,n-k).
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-1b432492072e2170 · 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"
    }
  }
}

Certificate

basis_map, SHA-256 7f48214f4745d3498fb76f5e85d8c569181ab239f9033480f84e310a708c48ee, 12,524 bytes (2,186 compressed); download

polytool replayed the certificate when the step was written.

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