Proof step

Geometric basis map (elementary)

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

Concludes

Premises

Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).
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-6b58a9068ba19d7f · 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"
    }
  }
}

Certificate

basis_map, SHA-256 d24c5bc825816cb3fe5f5e504fcdfa47171b6ef3cdfb6231be31af21fcbcfd5e, 12,901 bytes (2,244 compressed); download

polytool replayed the certificate when the step was written.

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