Proof step e-9cfbf7a52f4ba322

preserver_image reversal, shift 0 → concludes about Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318). 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

• 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 col… (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 3adeeac61cf9a6a0d93ca8f2420bffea3c23ab8f548151288439f442afde6c62, 7,360 bytes (2,127 compressed); download JSON

Cited by

• n-0d55e0bb3c384646 (real_rooted)
• n-0d55e0bb3c384646 (one_signed_coefficients)
• n-0d55e0bb3c384646 (hadamard_kernel)