Proof step e-d527982dc7c0aa3b

preserver_image reversal, shift 0 → concludes about Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n. JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":1,\"first_degree\":0,\"step\":1}}"
}

Premises

• Reflected triangle of Stirling numbers of 2nd kind, S(n,n-k+1), n >= 1, 1 <= k <= n. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 596bc68969efdff15869e939ac765b0d4f31f0dfeab9f3ae4ea503c510c809e9, 10,508 bytes (2,658 compressed); download JSON

Cited by

• n-3cb22164e2f83fe1 (one_signed_coefficients)
• n-3cb22164e2f83fe1 (hadamard_kernel)
• n-3cb22164e2f83fe1 (real_rooted)