Proof step e-9d8ee33f10e795ac

basis_map A013609 → concludes about basis_map_A013609 of Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 co… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 col… (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 9de2fb87ac8772b0a137df133d04f694f0d3ec6c1eec26c98f7c8070f6a3c327, 11,644 bytes (2,079 compressed); download JSON

Cited by

• n-da6d41f828bec089 (real_rooted)
• n-da6d41f828bec089 (one_signed_coefficients)
• n-da6d41f828bec089 (hadamard_kernel)