Proof step

Geometric basis map (elementary)

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

Concludes

Premises

Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-567d6f79aa6a87e5 · JSON

Operation

Image under a basis map u^k -> P_k

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

Claims

{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

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

Certificate

basis_map, SHA-256 48f3b44ddf9a5035777cdf56a6533a052e00539a3ce60ac1e992ede1dfb268ee, 13,480 bytes (2,557 compressed); download

polytool replayed the certificate when the step was written.

Cited by