Proof step e-5b79b5b4d4f1c577

preserver_image affine, shift 0 → concludes about Even-numbered rows of Pascal's triangle. 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

• basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a tr… (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 2a396086b003b92c3cd0ac59655e19daaf8ee741212c4de518f2916e0b9cad3b, 4,893 bytes (1,534 compressed); download JSON

Cited by

• n-08f49539099949d5 (one_signed_coefficients)
• n-08f49539099949d5 (hadamard_kernel)
• n-08f49539099949d5 (real_rooted)