Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes

Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).

Premises

Triangle read by rows: row n consists of n zeros followed by n!.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Lean

RealRooted Polynomial.Splits.comp_of_degree_le_one

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-ecf0fd7fe9e4692a · 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 c75609c404fbfdb05fda515986cb8c29a95e2293ae6f06c0f0026eb509f76c8a, 7,629 bytes (2,241 compressed); download

polytool replayed the certificate when the step was written.

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