Proof step e-b29f35705824bef6

parent_provers paper_theorem → concludes about Triangle read by rows: T(n,k) = |s(n,n+1-k)|, where s(n,k) are the signed Stirling numbers of the first kind A008276 (1 <= k <= n; in other words, the unsigned… JSON

Theorem

Parent-row provers of polytool polytool ?

Operation

Shared parent provers on the node's own rule

{
  "operation": "parent_provers",
  "route": "paper_theorem"
}

Premises

None: this step is a direct theorem check.

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "previous_interlaces_next" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: parent_provers, SHA-256 4dd6f46ba6c2bbe56e3cf1b985c1b401e3e63c8a5eb86ee6f135f8bdf664a0b7, 1,980 bytes (852 compressed); download JSON

Cited by

• n-4d60c3dd8627c01d (one_signed_coefficients)
• n-4d60c3dd8627c01d (hadamard_kernel)
• n-4d60c3dd8627c01d (interlacing)
• n-4d60c3dd8627c01d (real_rooted)