Proof step e-0f9b3c3168d8e647

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: T(n,k) = 2^floor(n/2)*binomial(n-1,k-1). 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) = 2^floor(n/2)*binomial(n-1,k-1). (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 1b640436650e8ff12f6763fa3ab9ff4e99cb6b2236bba2d3fb18d1b31432beaa, 6,929 bytes (1,413 compressed); download JSON

Cited by

• n-8f0d536701873284 (real_rooted)
• n-8f0d536701873284 (one_signed_coefficients)
• n-8f0d536701873284 (hadamard_kernel)