Proof step e-52b4a42a5c10d66a

basis_map_theorem → concludes about Triangle of numbers T(n,k) = k!*Stirling2(n,k) read by rows (n >= 1, 1 <= 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, 1]", "output_interval": "[-1, 0]", "statement": "source [-1, 1], 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 09660bb5e95fa847626e299ea1f7161091418e7ef04518e462503c237048e9f8, 2,472 bytes (945 compressed); download JSON

Cited by

• n-d938c1937a93c4df (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