Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes

Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*1^j.

Premises

Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*1^j.
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-5c75ec2792542a1c · 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"
    }
  }
}

{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

preserver_image, SHA-256 b04f1f1c27b879f78fb6acd38e43a1d727c1e8c04be6c2e375a4fdf18cae9166, 9,163 bytes (2,640 compressed); download

polytool replayed the certificate when the step was written.

Cited by