Proof step e-4e4f839e32ed0b09

basis_map_theorem → concludes about Triangle read by rows, S_3(n, k) where S_m(n, k) are the Stirling-Frobenius subset numbers of order m; n >= 0, k >= 0. JSON

Theorem

Ray basis map theorem [MW08, Thm 2] polytool RealRooted rayBasisMap_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": "(-inf, 2]", "output_interval": "(-inf, 0]", "statement": "source (-inf, a + b h + kappa m] = (-inf, 2] with m = 0, target (-inf, 0]" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 f38b5b1b24c2dd84d5aff55ebd4a264e384eec5aaf61ce6fb8eae9e61407f06b, 2,039 bytes (875 compressed); download JSON

Cited by

• n-58f68e861f34b78a (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