Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes

Triangular array A066667 or A008297 unsigned and transposed.

Premises

basis_map_A008277 of Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded in incr…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Lean

RealRooted route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-81cf897b95e1d503 · JSON

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

preserver_image, SHA-256 21d6c1cf7ef26735e7dbcd82419a4285f8c80c5fe6cea1ce45f7caf43d9f1d47, 10,858 bytes (2,806 compressed); download

polytool replayed the certificate when the step was written.

Cited by

n-d55979c30b97975a (one_signed_coefficients)
n-d55979c30b97975a (hadamard_kernel)
n-d55979c30b97975a (real_rooted)