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_A013610 of Triangle of Bessel numbers read by rows: T(n,k) is the number of k-matchings of the complete graph 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-6364ebbb017f26b9 · 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 e0d7230542f693facce7db02f9f993fa94e33e294a2cd3a049dd3fbefc598fe0, 10,320 bytes (2,995 compressed); download
polytool replayed the certificate when the step was written.
Cited by