Proof step e-f409e7a544612dfe

preserver_image affine, shift 0 → concludes about Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros). 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

• Triangular array binomial(2*n-k, k), k=0..n, n >= 0. (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 c1866b9ae418e793320bd8192d9c0ee04ffca49fdd7f5ea3c341c0ab1f42657c, 13,998 bytes (3,414 compressed); download JSON

Cited by

• n-fac4d4a000d744e8 (real_rooted)
• n-fac4d4a000d744e8 (one_signed_coefficients)
• n-fac4d4a000d744e8 (hadamard_kernel)
• n-fac4d4a000d744e8 (interlacing)