Proof step e-7ca9df991456824b

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Triangular array read by rows: T(n,k) = binomial(n,2)*binomial(n,k), n>=0, 0<=k<=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

• Triangular array read by rows: T(n,k) = binomial(n,2)*binomial(n,k), n>=0, 0<=k<=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 8e31f369951abfa32908ed9924b796ef713037be5dd1ee5a049f95e592c4ac22, 7,492 bytes (2,067 compressed); download JSON

Cited by

• n-66b456586fffaa5f (one_signed_coefficients)
• n-66b456586fffaa5f (hadamard_kernel)
• n-66b456586fffaa5f (real_rooted)