Proof step e-726c0b03589eafe2

preserver_image affine, shift 0 → concludes about Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 001 (n,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\":\"1/8\",\"intercept\":\"-1/8\"}"
}

Premises

• Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318). (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 39ed329647f586bed64b169470b8c8ac78a03c0ed689d523c8a292eb47adceed, 7,406 bytes (2,241 compressed); download JSON

Cited by

• n-512e5935bc8384f1 (real_rooted)