Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver mobius, shift 0

Concludes
mobius_x_over_x_plus_one of basis_map_A013609 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, …
Premises
Theorem
polytool ?
Lean
RealRooted route fTransform RealRooted.splits_fPolynomial
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-91df93c7fbe09f51 · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"mobius\",\"a\":\"1\",\"b\":\"0\",\"c\":\"1\",\"e\":\"1\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "lower": {
      "closed": true,
      "value": "-1"
    },
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
preserver_image, SHA-256 1b50c5128f473322c7316caccd2c275305c2e723be1c35ac4957b1378273b35b, 16,909 bytes (4,531 compressed); download
polytool replayed the certificate when the step was written.
Cited by