Proof step e-0e9e334768ea0a35

preserver_image reversal, shift 0 → concludes about Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 column k lists two zero… JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

Operation

Image under a real-rootedness preserver

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

Premises

• Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

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

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 c6c6868d320f3daa7684a8f7277f1941181a21edd6458136172e0caa90063e9a, 6,946 bytes (2,096 compressed); download JSON

Cited by

• n-67a75673619cc276 (real_rooted)
• n-67a75673619cc276 (one_signed_coefficients)
• n-67a75673619cc276 (hadamard_kernel)