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 theta_plus_one of Triangle read by rows: T(n,k) (n >= 1, 0 <= k <= ceiling(n/2)-1) = number of permutations of [n] with k peaks.
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-32af5deb30df2991 · 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 f2ee5c67c461cc875d48c193304381b31d154007e6e8c220295f868c644e11ae, 8,906 bytes (2,208 compressed); download
polytool replayed the certificate when the step was written.
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