Proof step e-13dcb978bba71940

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 e9dd4b8063e2c0fe3bcfdd922f78a45dd118fb9327f11af64fd70374cfc3193a, 6,862 bytes (1,392 compressed); download JSON

Cited by

• n-9466c8441e24ce06 (real_rooted)
• n-9466c8441e24ce06 (one_signed_coefficients)
• n-9466c8441e24ce06 (hadamard_kernel)