Proof step e-587b84b5d7cc5e21

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: T(n,k) = binomial(k,n-k). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle read by rows: T(n,k) = binomial(k,n-k). (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 e45908db78e778697106312305ee05caf9a759a88417349860d4fd7f72afa1c3, 11,582 bytes (2,150 compressed); download JSON

Cited by

• n-0552ada0abe44307 (real_rooted)
• n-0552ada0abe44307 (one_signed_coefficients)
• n-0552ada0abe44307 (hadamard_kernel)