Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013609

Concludes

Premises

Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-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-e5f2c21647599214 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Claims

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

{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 f9d437c485f8f8b2395e74314c2e89f81a9dcd0e7ec0b394945e9408242402bb, 10,248 bytes (2,284 compressed); download

polytool replayed the certificate when the step was written.

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