Proof step e-ee5cc8292e809076

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Number triangle T(n,k)=C(n,k)C(2,n-k). 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

• Number triangle T(n,k)=C(n,k)C(2,n-k). (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 fab386f967aabd90a124059149e27ed4c75a5daef211ab3625574d26758cfa0a, 7,205 bytes (1,968 compressed); download JSON

Cited by

• n-5a583a8eb9880032 (real_rooted)
• n-5a583a8eb9880032 (one_signed_coefficients)
• n-5a583a8eb9880032 (hadamard_kernel)