Proof step e-226103a223be7e17

basis_map A013610 → concludes about basis_map_A013610 of basis-map coefficients of Triangle read by rows: T(n,k) = binomial(k,n-k). shifted by x -> -x + 0 JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Triangle read by rows: T(n,k) = binomial(k,n-k). shifted by x -> -x + 0 (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 eedf64bb0f89c5e0ae4ab6bf8ad592ebfacde7575eb86f44f535d8e8c52cb687, 6,862 bytes (1,392 compressed); download JSON

Cited by

• n-96b6c636cb527859 (real_rooted)
• n-96b6c636cb527859 (one_signed_coefficients)
• n-96b6c636cb527859 (hadamard_kernel)