Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver mobius, shift 0

Concludes

basis_map_A013609 of Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical let…

Premises

basis_map_A007318 of Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n >= 1, 0 <= k <= n-1). A le…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Lean

RealRooted route fTransform RealRooted.splits_fPolynomial

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-b5b75057523b9d15 · JSON

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"mobius\",\"a\":\"1\",\"b\":\"0\",\"c\":\"1\",\"e\":\"1\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}

Claims

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

Certificate

preserver_image, SHA-256 c8eb9149fdfc8b3227c6dcd3f316c9f4eccbf982a5312d5c355e4fb01688ac59, 8,296 bytes (2,420 compressed); download

polytool replayed the certificate when the step was written.

Cited by

n-4a6fce4b90b6e934 (one_signed_coefficients)
n-4a6fce4b90b6e934 (hadamard_kernel)
n-4a6fce4b90b6e934 (real_rooted)