Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes
shift_x_plus_one of basis_map_A007318 of Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also…
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-0613c6a4c63d1807 · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "-1"
    }
  }
}
Certificate
preserver_image, SHA-256 d6c43c61db698def2988fc9c1895f1c2f3be7e48f47e8e9f0c6a4170d03f9755, 11,819 bytes (3,449 compressed); download
polytool replayed the certificate when the step was written.
Cited by