Proof step e-2ae8453bca041506

preserver_image affine, shift 0 → concludes about Triangle read by rows, related to clusters of type D. 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) = binomial(n, k)*binomial(n + 2, k). (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" } } }
• { "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 782a5033eb5a15112d7f841d8a3e5ce0189457265e9b570005041964fc768af8, 15,871 bytes (3,238 compressed); download JSON

Cited by

• n-5aa52e3acf29a627 (real_rooted)
• n-5aa52e3acf29a627 (one_signed_coefficients)
• n-5aa52e3acf29a627 (hadamard_kernel)
• n-5aa52e3acf29a627 (interlacing)