Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes

reversal of basis_map_A007318 of Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1).

Premises

basis_map_A007318 of Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-5, -1)

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-a1effaf0297b60b5 · 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": {
    "lower": {
      "closed": false,
      "value": "-1"
    },
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

preserver_image, SHA-256 b8c74b279e95afd3d282e2a5e616936cea9522205bbac8a1a410719472879a0f, 16,900 bytes (3,219 compressed); download

polytool replayed the certificate when the step was written.

Cited by

n-e9f75ddaed25275f (real_rooted)
n-e9f75ddaed25275f (one_signed_coefficients)
n-e9f75ddaed25275f (hadamard_kernel)