Proof step e-0f361da4a6c0f5b4

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 4ab1496896ca89b1223d1e14f094bc9b97d18b69cab945fbe1c519537ba20e69, 7,414 bytes (1,618 compressed); download JSON

Cited by

• n-1e0cd3ca23b1a82f (real_rooted)
• n-1e0cd3ca23b1a82f (one_signed_coefficients)
• n-1e0cd3ca23b1a82f (hadamard_kernel)