Proof step e-d4fed5f2404ee52f

basis_map_theorem → concludes about Triangle of numbers T(n,k) = k!*Stirling2(n,k) = A000142(k)*A048993(n,k) read by rows, T(n, k) for 0 <= k <= n. JSON

Theorem

Interval basis map theorem [MW08, Thm 2, Cor 3] polytool RealRooted intervalBasisMap_maps_realRootedIn_iff ?

Operation

Basis map theorem for the node's own rule

{
  "operation": "basis_map_theorem"
}

Premises

None: this step is a direct theorem check.

Claims

• { "claim": "basis_map_preserver", "input_interval": "[-1, 0]", "output_interval": "[-1, 0]", "statement": "source [-1, 0], target [-1, 0]" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 7ae9064d09bc8dacac5f5a6f3fc121eb6a22fc7b32bd750a7a90f0ac7c277f60, 2,501 bytes (950 compressed); download JSON

Cited by

• n-2cabfd060b04f15d (basis_map_preserver)

References

1. [MW08] Shi-Mei Ma and Yi Wang. q-Eulerian polynomials and polynomials with only real zeros. The Electronic Journal of Combinatorics, 15(1):Research Paper 17, January 2008. doi:10.37236/741