Proof step e-267456e89d3343d1

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 741e3ae4c4099cc41372069ff0d294615101b82ca328cd33a640bf613c21ba37, 6,885 bytes (1,399 compressed); download JSON

Cited by

• n-2b301932743053f0 (real_rooted)
• n-2b301932743053f0 (one_signed_coefficients)
• n-2b301932743053f0 (hadamard_kernel)