Proof step e-0a406e2d3e1f653c

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Triangle formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1. 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 formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1. (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 244700ff2a99ac1b6b8f34d21d4fc95b7d85eb9eec9764d9b000cee60d3a6554, 7,577 bytes (1,985 compressed); download JSON

Cited by

• n-ebbce5356dede62c (real_rooted)
• n-ebbce5356dede62c (one_signed_coefficients)
• n-ebbce5356dede62c (hadamard_kernel)