Proof step e-6dbd3471b7b80662

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Stirling2 triangle with scaled diagonals (powers of 2). 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

• Stirling2 triangle with scaled diagonals (powers of 2). (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 96207f1db2ed0f7b1ee5d4d23228489a34f9e811dd276d2f19a8c793ab6a5f44, 11,645 bytes (2,930 compressed); download JSON

Cited by

• n-7eb19ab4ebf03277 (real_rooted)
• n-7eb19ab4ebf03277 (one_signed_coefficients)
• n-7eb19ab4ebf03277 (hadamard_kernel)
• n-7eb19ab4ebf03277 (interlacing)