Proof step e-64d32b29af27d169

basis_map A013610 → concludes about basis_map_A013610 of Triangular array binomial(2*n-k, k), k=0..n, n >= 0. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangular array binomial(2*n-k, k), k=0..n, n >= 0. (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 fe31025beee2ea6c27a3daa33f20abd7183a4e9c07d6f21e1e23a8beebe32b36, 13,622 bytes (2,602 compressed); download JSON

Cited by

• n-17342fb8b400751e (real_rooted)
• n-17342fb8b400751e (one_signed_coefficients)
• n-17342fb8b400751e (hadamard_kernel)
• n-17342fb8b400751e (interlacing)