Proof step e-5428ec8f88838d6b

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Triangle read by rows: T(n,k) is the number of binary words of length n having degree of asymmetry equal to k (n >= 0; 0 <= k <= n/2). 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 read by rows: T(n,k) is the number of binary words of length n having degree of asymmetry equal to k (n >= 0; 0 <= k <= n/2). (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 3c8f1aac7e203cac27ea2d8acdb45777f3f296708b8c0d4bd5c73b73d94f4a4d, 6,544 bytes (1,885 compressed); download JSON

Cited by

• n-d321ff0d3bb39024 (real_rooted)
• n-d321ff0d3bb39024 (one_signed_coefficients)
• n-d321ff0d3bb39024 (hadamard_kernel)