Proof step e-99c1ee54068faff3

preserver_image reversal, shift 0 → concludes about reversal of Triangular array binomial(2*n-k, k), k=0..n, n >= 0. 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\":0,\"step\":1}}"
}

Premises

• Triangular array binomial(2*n-k, k), k=0..n, n >= 0. (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 8a3132705cdb54c0cf5c2a7cd0587819eb7a13ee9a5bf5e3ca37951a14bb8c55, 12,705 bytes (3,075 compressed); download JSON

Cited by

• n-4c232e962100ae75 (real_rooted)
• n-4c232e962100ae75 (one_signed_coefficients)
• n-4c232e962100ae75 (hadamard_kernel)