Proof step e-190c283dd8b47413

preserver_image affine, shift 0 → concludes about 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. JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): Polynomial.Splits.comp_of_degree_le_one

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

Premises

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

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-2" }, "upper": { "closed": false, "value": "-1" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 56c12d7a25b3914b4b58dc2448bab231c1513d4f83fa6d4dbc595b57363b8aa2, 20,237 bytes (3,780 compressed); download JSON

Cited by

• n-07af2e6e3c9f0c77 (hadamard_kernel)
• n-07af2e6e3c9f0c77 (interlacing)
• n-07af2e6e3c9f0c77 (real_rooted)
• n-07af2e6e3c9f0c77 (one_signed_coefficients)