Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013611

Concludes
basis_map_A013611 of gamma_polynomial of Triangle T(n, k) is coefficient of z^n*w^k in 1/(1 - 2*z - 2*w - 2*z*w) read by rows in order 00, 10, 01, 20, 11, 02, …
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-72549cd00f2df053 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013611",
  "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 ab0ed411bffde8fce0e6de6585be1bfc3c40b40ea26cbf15ebdb3c9ab52f667b, 14,433 bytes (2,865 compressed); download
polytool replayed the certificate when the step was written.
Cited by