Proof step e-a8162231721a7380

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Triangle of B-analogs of Stirling numbers of 2nd kind. 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 B-analogs of Stirling numbers of 2nd kind. (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 47521f03b0dde58ceb673379febca24311acc534df4aad85a49203ff740b9f9f, 11,767 bytes (2,957 compressed); download JSON

Cited by

• n-0c5ba5f813be2bea (real_rooted)
• n-0c5ba5f813be2bea (one_signed_coefficients)
• n-0c5ba5f813be2bea (hadamard_kernel)
• n-0c5ba5f813be2bea (interlacing)