Proof step

Geometric basis map (elementary)

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

Concludes

Premises

Triangle T(n,k) with diagonals T(n,n-k) = binomial(n, 2*k).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-7709ed90759c2bb5 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

basis_map, SHA-256 04732438818b4e52fbf7f607e03f424d88ae60bd57a8c0557f0fdea3a503ec6a, 11,868 bytes (2,209 compressed); download

polytool replayed the certificate when the step was written.

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