Proof step e-17c52917511dc051

preserver_image affine, shift 0 → concludes about Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j). 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

• binomial (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 05fddca10fbc13a93d6b9f815f3c8aeaac37d299a1f4b80bf5666624ec3bdbc5, 9,112 bytes (2,589 compressed); download JSON

Cited by

• n-af754f07daf65b5e (one_signed_coefficients)
• n-af754f07daf65b5e (hadamard_kernel)
• n-af754f07daf65b5e (real_rooted)
• n-af754f07daf65b5e (interlacing)