Proof step e-fa68694d112454ed

basis_map A026729 → concludes about Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A026729",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in [0, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "lower": { "closed": true, "value": "-4" }, "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 9453defebbe177b08bd7fa4ba9956ed37ac1393e3453938a3ba86b38514eb745, 13,475 bytes (2,062 compressed); download JSON

Cited by

• n-392f49b496f79fbf (one_signed_coefficients)
• n-392f49b496f79fbf (hadamard_kernel)
• n-392f49b496f79fbf (real_rooted)