Proof step e-169cfb9127a1a777

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows. T(n, k) = binomial(n, k)*binomial(n - 1, n - k - 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(n, k)*binomial(n - 1, n - k - 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": 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 9618c2d63a8c393a533f07ecc3130e86fc94c7c0c102c53b613a7acd7408c881, 14,558 bytes (2,761 compressed); download JSON

Cited by

• n-3897d3bccfbe11da (real_rooted)
• n-3897d3bccfbe11da (one_signed_coefficients)
• n-3897d3bccfbe11da (hadamard_kernel)
• n-3897d3bccfbe11da (interlacing)