Proof step e-b19ded6a55d5da85

basis_map A013609 → concludes about basis_map_A013609 of Triangle T(n,k), read by rows given by [1,0,1,0,0,0,0,0,0,...] DELTA [0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A08493… 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(n + k, 2*k). (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 2, "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 fe9026e54e174ca3eb1ff199a8dbbece8b18bd044b4a69ea31fb0e2246e41f95, 13,345 bytes (2,520 compressed); download JSON

Cited by

• n-1852b727a5d6b55d (interlacing)
• n-1852b727a5d6b55d (real_rooted)
• n-1852b727a5d6b55d (one_signed_coefficients)
• n-1852b727a5d6b55d (hadamard_kernel)