Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes

Triangle of coefficients in expansion of (14 + x)^n.

Premises

basis_map_A007318 of Triangle whose (i,j)-th entry is binomial(i,j)*12^(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-b56f3865ea2acff7 · 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 d0cb0efb6743192ef8d44035b06be775e7c28d22549bd96471a7eda5b265cacd, 9,197 bytes (2,657 compressed); download

polytool replayed the certificate when the step was written.

Cited by