Proof step e-56c0c02612a8191c

preserver_image affine, shift 0 → concludes about Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order). 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

• A convolution triangle of numbers based on A001906 (even-indexed Fibonacci numbers). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-5, -1)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-6" }, "upper": { "closed": false, "value": "-2" } } }
• { "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 8dc4494a1e2ed5342d45b61af8e2727cad6124c0afc55155169f37cd84abda33, 18,272 bytes (3,625 compressed); download JSON

Cited by

• n-30cb3cad216ed189 (one_signed_coefficients)
• n-30cb3cad216ed189 (hadamard_kernel)
• n-30cb3cad216ed189 (real_rooted)
• n-30cb3cad216ed189 (interlacing)