Proof step e-2e0332653cdf3eaa

preserver_image affine, shift 0 → concludes about basis_map_A007318 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-4*k)!*4^k) for n>=4*k>=0. 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, read by rows, where T(n,k) = n!/(k!*(n-4*k)!*4^k) for n>=4*k>=0. (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 9744540f386ac7ec696f2af6287a3a84450b0e5a4a5f337074a34f25fa5beec8, 6,860 bytes (2,043 compressed); download JSON

Cited by

• n-aa4f19523cc05a57 (one_signed_coefficients)
• n-aa4f19523cc05a57 (hadamard_kernel)
• n-aa4f19523cc05a57 (real_rooted)