Proof step e-6f6524a2909f4dfb

basis_map A013611 → concludes about basis_map_A013611 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": "A013611",
  "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 6db3588ae686c2a2f048e03613bc5537aba12c714352650b76e3a685acac5285, 6,885 bytes (1,402 compressed); download JSON

Cited by

• n-98c21bd2a6c7c1d4 (real_rooted)
• n-98c21bd2a6c7c1d4 (one_signed_coefficients)
• n-98c21bd2a6c7c1d4 (hadamard_kernel)