Proof step e-9477b3c3a3760be1

basis_map A007318 → concludes about shift_x_plus_one of Triangle read by rows: T(n,k) is the number of binary words of length n having degree of asymmetry equal to k (n >= 0; 0 <= k <= n/2). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle read by rows: T(n,k) is the number of binary words of length n having degree of asymmetry equal to k (n >= 0; 0 <= k <= n/2). (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 9d002a92faa5578a8a83ab2fb821c87c198a1bb9e75885e13a3d08ac8029d157, 6,885 bytes (1,397 compressed); download JSON

Cited by

• n-d321ff0d3bb39024 (one_signed_coefficients)
• n-d321ff0d3bb39024 (hadamard_kernel)
• n-d321ff0d3bb39024 (real_rooted)