Proof step e-3adfaf26de79e7ad

preserver_image reversal, shift 0 → concludes about Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions. 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

• Triangle read by rows: T(n,k) is the number of Schroeder paths of semilength n containing exactly k peaks but no peaks at level one (n >= 1… (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 51333a878e2bd8b204f6a5718eebd086154a3cc596a981fca12219f36a405260, 14,147 bytes (3,373 compressed); download JSON

Cited by

• n-66e2c3448245b0b7 (one_signed_coefficients)
• n-66e2c3448245b0b7 (hadamard_kernel)
• n-66e2c3448245b0b7 (real_rooted)