Proof step e-b7289e9f518eca68

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 25e702a38bd51a1f5cc91a582c9ee283d209b6d8255e2262ebdb520c9300b118, 7,400 bytes (1,621 compressed); download JSON

Cited by

• n-cf97dd8f766eb0a5 (real_rooted)
• n-cf97dd8f766eb0a5 (one_signed_coefficients)
• n-cf97dd8f766eb0a5 (hadamard_kernel)