Proof step e-54689045adf560eb

basis_map A008288 → concludes about basis_map_A008288 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-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A008288",
  "operation": "basis_map"
}

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": true, "exact": { "radicand": "2", "rational_part": "-3", "sqrt_coefficient": "-2" }, "value": "-1564556493/268435456" }, "upper": { "closed": true, "exact": { "radicand": "2", "rational_part": "-3", "sqrt_coefficient": "2" }, "value": "-46056243/268435456" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 0034aa3aaf19ffec5c9f82ee70e355aa21cdbe681d002fac0414c9385012b3c4, 24,204 bytes (3,195 compressed); download JSON

Cited by

• n-de8e55fb070a3937 (one_signed_coefficients)
• n-de8e55fb070a3937 (hadamard_kernel)
• n-de8e55fb070a3937 (real_rooted)