Proof step e-ba7f4c6c74dd05c0

basis_map A007318 → concludes about 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": "A007318",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of 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, 1]

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 01f87e6ceed8a148e77e0f5407da3a7bbe20d024db74ce9db021329563186d61, 11,588 bytes (2,155 compressed); download JSON

Cited by

• n-21854f4257effb01 (real_rooted)
• n-21854f4257effb01 (one_signed_coefficients)
• n-21854f4257effb01 (hadamard_kernel)