Proof step

Geometric basis map (elementary)

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

Concludes

shift_x_plus_one of gamma_polynomial of narayana

Premises

gamma_polynomial of narayana
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-4e65d47143297ee9 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "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 23f1b6ed847c6080d40aa5b30c9b0c628be1865253e150ede8fcbefb7411a163, 14,925 bytes (2,951 compressed); download

polytool replayed the certificate when the step was written.

Cited by