Proof step

Geometric basis map (elementary)

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

Concludes

Premises

Triangular T(n,k) = T(n-1, k) + T(n-1, k-1) + 5*T(n-2, k-1), read by rows.
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-40e926fe6770bb52 · 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": 3,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 aa85fb0e8e58843e33272bbc496424708ea34af0b08bc2777e0244d42cf21a08, 14,736 bytes (2,801 compressed); download

polytool replayed the certificate when the step was written.

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