Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes
shift_x_plus_one of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shi…
Premises
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-c143ae65fcce52cb · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":1,\"first_degree\":0,\"step\":1}}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
preserver_image, SHA-256 af3f888b56cdb8943c34cfd99d9391c7439d32ac7b4ea2d23336043cad965a6e, 5,070 bytes (1,568 compressed); download
polytool replayed the certificate when the step was written.
Cited by