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 Triangle read by rows: T(n,k) is the number of words over alphabet {0,1,2,3} having exactly k occurrences of the string 01, where n>=0 and …
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-3c630cd2594244dd · 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 b3ec8aebd92c8a22ce380e971a50982437e0541049d3cf9cf0e368eeea145377, 10,443 bytes (3,023 compressed); download
polytool replayed the certificate when the step was written.
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