Proof step e-9c0dd75b125bab92

preserver_image reversal, shift 0 → concludes about Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2. 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

• a(n) = 1 if n is a triangular number, otherwise 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 c2cd48275a8647bcd0d8bcef2dee3872eecc426fbb4f9a24c8a181ec7963e1a0, 6,352 bytes (1,875 compressed); download JSON

Cited by

• n-511a2225fa2191c9 (real_rooted)
• n-511a2225fa2191c9 (one_signed_coefficients)
• n-511a2225fa2191c9 (hadamard_kernel)