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 derivative of Triangle read by rows: T(n,k) are the coefficients of Charlier polynomials: A046716 transposed, for 0 <= k <= n.
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-8623d6abd5f26497 · 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": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "-1"
    }
  }
}
Certificate
preserver_image, SHA-256 f5a56e4c958a2329bea1db7ff84f81f3f6dead9b531b2d7c068191b8739979ae, 8,182 bytes (2,022 compressed); download
polytool replayed the certificate when the step was written.
Cited by