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 - 1, k - 1)*binomial(n + k, k).
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-ad0ec5ec50db3cb1 · 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 f9b168ba871a3541d0e90229b90ab6d9eaed0fd21e38aa8147d3585a1f812b93, 16,266 bytes (3,151 compressed); download

polytool replayed the certificate when the step was written.

Cited by