Proof step e-fb2d67190f0fa658

basis_map A013611 → concludes about basis_map_A013611 of Triangle T(n,k) = n!*binomial(n-1, k-1) for 1 <= k <= n, read by rows. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle T(n,k) = n!*binomial(n-1, k-1) for 1 <= k <= n, read by rows. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "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 40a09bc52fc86a782638b05b65b27c10fa8831b8462d382859cb0474f99c8971, 7,400 bytes (1,619 compressed); download JSON

Cited by

• n-4766ad62f3b3a125 (real_rooted)
• n-4766ad62f3b3a125 (one_signed_coefficients)
• n-4766ad62f3b3a125 (hadamard_kernel)