Proof step e-3cb5f3d64c4bb317

basis_map A056242 → concludes about Triangle read by rows: T(n,k) = number of k-part order-consecutive partition of {1,2,...,n} (1 <= k <= n). JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A056242",
  "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": "-1" }, "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 02cb55ae901e2ce091cc2f0a0b356e3fb98e174fbdf710f8981844185c7f7a6b, 11,437 bytes (1,967 compressed); download JSON

Cited by

• n-2821c21537bbbcdd (real_rooted)
• n-2821c21537bbbcdd (one_signed_coefficients)
• n-2821c21537bbbcdd (hadamard_kernel)