Proof step e-4fb0c58de9dbd95f

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Triangle of coefficients of Gaussian polynomials [2n+1,1]_q represented as finite sum of terms (1+q^2)^k*q^(g-k), where k = 0,1,...,g with … 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 of coefficients of Gaussian polynomials [2n+1,1]_q represented as finite sum of terms (1+q^2)^k*q^(g-k), where k = 0,1,...,g with … (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-2, 2)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-3" }, "upper": { "closed": false, "value": "1" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 36e2db3d2745b1d4ee84edbaa3ddf01091b9cabb25c3e44fd2122817235427be, 18,256 bytes (3,323 compressed); download JSON

Cited by

• n-35e99788be157971 (real_rooted)
• n-35e99788be157971 (interlacing)