Proof step e-0c475173369de966

preserver_image reversal, shift 0 → concludes about reversal of Triangle read by rows: 3-Stirling numbers of the second kind. 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\":1,\"first_degree\":0,\"step\":1}}"
}

Premises

• Triangle read by rows: 3-Stirling numbers of the second kind. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "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 733d5d056fcea19514a397e0813bdebc565dce6f09f5877c9908f1357ef0022e, 10,403 bytes (2,623 compressed); download JSON

Cited by

• n-06404fc73ac5a6a1 (real_rooted)
• n-06404fc73ac5a6a1 (one_signed_coefficients)
• n-06404fc73ac5a6a1 (hadamard_kernel)