Proof step

Geometric basis map (elementary)

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

Concludes

Premises

Triangle read by rows, T(n,k) = (n+1)*binomial(n-1,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-39c185df7b68a75c · 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": 2,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 2ea929ac2c8eabf779394649a1932a3d2cd194c318e11ac585fb63caf0623462, 16,710 bytes (3,307 compressed); download

polytool replayed the certificate when the step was written.

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