Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes

reversal of Triangle of Dyck paths counted by number of long interior inclines.

Premises

Triangle of Dyck paths counted by number of long interior inclines.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Lean

RealRooted route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-bd3c446520e346b3 · JSON

Operation

Image under a real-rootedness preserver

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

Claims

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

Certificate

preserver_image, SHA-256 230090e7efb8062cc16e25583e3390cc0b3ba5ccf2041aef5a84b84708249ed7, 17,305 bytes (4,202 compressed); download

polytool replayed the certificate when the step was written.

Cited by

n-c7016e67374634ec (real_rooted)
n-c7016e67374634ec (one_signed_coefficients)
n-c7016e67374634ec (hadamard_kernel)