Proof step e-56752775b3d97dc0

basis_map A007318 → concludes about basis_map_A007318 of Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,...] DELTA [3,-2,-1,0,0,0,0,0,0,...] where DELTA is the operator … JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,...] DELTA [3,-2,-1,0,0,0,0,0,0,...] where DELTA is the operator d… (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 665b82d57e53ad444f72a8bb27c6691f812713fbdb0b588f2c110612c3ce9464, 6,927 bytes (1,403 compressed); download JSON

Cited by

• n-67db2effba549c79 (real_rooted)
• n-67db2effba549c79 (one_signed_coefficients)
• n-67db2effba549c79 (hadamard_kernel)