Proof step e-16a1260593e0941e

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 k-matchings of the corona K'(n) of the complete graph K(n) and the complete graph K(… 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 k-matchings of the corona K'(n) of the complete graph K(n) and the complete graph K(1); in o… (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 0eb8d9426072d756abcd61db32348bc7d2ad9ad89c03e33b79377ad037b8cac8, 16,339 bytes (3,678 compressed); download JSON

Cited by

• n-b37fb34e5b5db4ed (one_signed_coefficients)
• n-b37fb34e5b5db4ed (hadamard_kernel)
• n-b37fb34e5b5db4ed (real_rooted)