Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes

reversal of basis_map_A007318 of Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions.

Premises

basis_map_A007318 of Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-2, -1)

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-e5739c6a1dde738f · 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": {
    "lower": {
      "closed": false,
      "value": "-1"
    },
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

preserver_image, SHA-256 58eb37bb571e215c851fc0dc0209f93bb5f47296f0b6c4966cc9d2616677ac03, 19,503 bytes (3,848 compressed); download

polytool replayed the certificate when the step was written.

Cited by

n-c0e24188ccfeaae9 (one_signed_coefficients)
n-c0e24188ccfeaae9 (hadamard_kernel)
n-c0e24188ccfeaae9 (real_rooted)