Proof step

Geometric basis map (elementary)

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

Concludes

Premises

derivative of Triangle of coefficients in expansion of (1+3*x)^n.
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-1345394fdb10146f · 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"
    }
  }
}

{
  "claim": "interlacing",
  "from_index": 2,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 1379c464b380709b2f0b9d0d5b80d12c589dc6b7ea4faa9ee4ec482c05a3493c, 15,247 bytes (2,816 compressed); download

polytool replayed the certificate when the step was written.

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