Proof step e-c5ecb99958d189a5

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Triangle T(n,k) read by rows: number of size-k antisymmetric subsets of {1,2,...,n}. JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): Polynomial.Splits.comp_of_degree_le_one

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

Premises

• Triangle T(n,k) read by rows: number of size-k antisymmetric subsets of {1,2,...,n}. (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": "-1" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 770f7f7d9d13b944502e239ddd96e14fedb3a8cc30b5ed03155cdc5c4642c9c4, 6,472 bytes (1,836 compressed); download JSON

Cited by

• n-4e8690098ee9d7b4 (real_rooted)
• n-4e8690098ee9d7b4 (one_signed_coefficients)
• n-4e8690098ee9d7b4 (hadamard_kernel)