Proof step e-b8bffdca39e5528f

preserver_image affine, shift 0 → concludes about basis_map_A007318 of Triangle of even numbered entries of odd numbered rows of Pascal's triangle A007318. 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 even numbered entries of odd numbered rows of Pascal's triangle A007318. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "-1" } } }
• { "claim": "interlacing", "from_index": 2, "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 e5eda7f6242ab94b085c49c759fa9a078474efb83cd415ac22ace15276ba09cc, 14,843 bytes (3,526 compressed); download JSON

Cited by

• n-2887a9a5b94917e3 (one_signed_coefficients)
• n-2887a9a5b94917e3 (hadamard_kernel)
• n-2887a9a5b94917e3 (interlacing)
• n-2887a9a5b94917e3 (real_rooted)