Proof step e-fa986ad01f1c1b33

basis_map A013611 → concludes about basis_map_A013611 of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• 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 (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "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 3497ffbbd02fc783684eb096bd57c87a3bcf23bf7e87db2a576738644a074e4b, 11,662 bytes (2,189 compressed); download JSON

Cited by

• n-e2ca539e0aa62c2f (real_rooted)
• n-e2ca539e0aa62c2f (one_signed_coefficients)
• n-e2ca539e0aa62c2f (hadamard_kernel)