Proof step e-e61ce0e3d93770a8

preserver_image mobius, shift 0 → concludes about mobius_x_over_x_plus_one 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 identi… JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route fTransform RealRooted.splits_fPolynomial

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}}"
}

Premises

• 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 lett… (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": { "lower": { "closed": true, "value": "-1" }, "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 932ad22305fa3a500c11075ed848da5e4d4efac61ede9f636cead4a11f65fe61, 8,268 bytes (2,394 compressed); download JSON

Cited by

• n-4575a0f9ca60b9ab (real_rooted)
• n-4575a0f9ca60b9ab (one_signed_coefficients)
• n-4575a0f9ca60b9ab (hadamard_kernel)