Proof step e-fcd19baf8f835cf0

basis_map A007318 → concludes about 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": "A007318",
  "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 (-inf, 1]

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 d5d9576b47c874c4596b3ce911027452c4f2b3f9ea61cdc7b8376e6d8fded954, 11,671 bytes (2,194 compressed); download JSON

Cited by

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