Proof step e-49766d0fffe14f49

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows: T(n,k) = binomial(2n+1, 2k+1). 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) = binomial(2n+1, 2k+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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 7a98a3df96ba0341496f6f62c8c9d8e9d17c7a7be380340dda95c8baea6abc1b, 13,634 bytes (2,583 compressed); download JSON

Cited by

• n-8cbd6010e0efad10 (real_rooted)
• n-8cbd6010e0efad10 (one_signed_coefficients)
• n-8cbd6010e0efad10 (hadamard_kernel)
• n-8cbd6010e0efad10 (interlacing)