Proof step e-9b2a752e203a2a8f

basis_map_theorem → concludes about Triangle read by rows, k!*S_4(n, k) where S_m(n, k) are the Stirling-Frobenius subset numbers of order m; n >= 0, k >= 0. 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, 3]", "output_interval": "[-1, 0]", "statement": "source [-1, 3], 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 b9198b30bbbb0b0351af1ac3670d3d84b6f391758c01df6fdb6e717da56f6138, 2,511 bytes (974 compressed); download JSON

Cited by

• n-f425461cbf5769b3 (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