Proof step e-09eb0f66de37936d

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Array T(m,n) read by ascending antidiagonals: T(m,n) = m*binomial(n+m-2, n-1) for m, n >= 1. 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

• Array T(m,n) read by ascending antidiagonals: T(m,n) = m*binomial(n+m-2, n-1) for m, 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": "-1" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 763390327e222593e83e0455cfc9616d738b8b3fef209b090ad63e086db477a2, 10,847 bytes (2,944 compressed); download JSON

Cited by

• n-4b03a2849503b9e9 (real_rooted)
• n-4b03a2849503b9e9 (one_signed_coefficients)
• n-4b03a2849503b9e9 (hadamard_kernel)