Proof step e-e6ead7ccbecb2d32

basis_map A013611 → concludes about basis_map_A013611 of Triangle T(n, k) read by rows: T(n, k) = Sum_{j=0..n} binomial(j, n-k) * |Stirling1(n, n-j)|. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle T(n, k) read by rows: T(n, k) = Sum_{j=0..n} binomial(j, n-k) * |Stirling1(n, n-j)|. (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 a65b2f6e8572d585cb5171b1cef845ea3fccc433e625302ac79a42dd265bf0d1, 7,414 bytes (1,617 compressed); download JSON

Cited by

• n-054881b8a1092a7d (real_rooted)
• n-054881b8a1092a7d (one_signed_coefficients)
• n-054881b8a1092a7d (hadamard_kernel)