Proof step e-fa0bf0c51be28c3f

preserver_image affine, shift 0 → concludes about basis_map_A007318 of Triangle T(n,k) = n!/(k!*(n-3*k)!), for n >= 3*k >= 0, read by rows. 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 T(n,k) = n!/(k!*(n-3*k)!), for n >= 3*k >= 0, read by rows. (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 ab4470ea9dba905a0a7e57b4156feaa1b3cbcefe1edb41e5fe23d6440cc1cc7c, 6,743 bytes (2,019 compressed); download JSON

Cited by

• n-90bcb80ace6b055d (one_signed_coefficients)
• n-90bcb80ace6b055d (hadamard_kernel)
• n-90bcb80ace6b055d (real_rooted)