Proof step e-501bbcb2ca148024

basis_map A013611 → concludes about basis_map_A013611 of T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows. (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 e76de6759c75edd22c9cc8a37bbdf3c998fa1f1a821f473d3f0b1d77f7297ecc, 13,675 bytes (2,560 compressed); download JSON

Cited by

• n-9ed8bdf5901d9584 (real_rooted)
• n-9ed8bdf5901d9584 (one_signed_coefficients)
• n-9ed8bdf5901d9584 (hadamard_kernel)
• n-9ed8bdf5901d9584 (interlacing)