Proof step e-43029c72e0d48967

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n). (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 64384484af6b5391bc4a0e6fa6a85f2780e41c5a682d94d5dbe5d2ffa9b4d05c, 10,652 bytes (2,339 compressed); download JSON

Cited by

• n-badb483b8a863e57 (real_rooted)
• n-badb483b8a863e57 (one_signed_coefficients)
• n-badb483b8a863e57 (hadamard_kernel)
• n-badb483b8a863e57 (interlacing)