Proof step e-9efc939e395fae07

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 0c4cd2b0dcb096730f5df93eb6275495f14c6323ba90bb708579ace6b21f68fe, 14,554 bytes (2,755 compressed); download JSON

Cited by

• n-c2b0d68b9e568dde (interlacing)
• n-c2b0d68b9e568dde (real_rooted)
• n-c2b0d68b9e568dde (one_signed_coefficients)
• n-c2b0d68b9e568dde (hadamard_kernel)