Proof step e-982f957c1008df8b

basis_map_theorem → concludes about Triangular array read by rows. T(n,k) = A008277(n,k)*2^k; n >= 1, 1 <= k <= n. 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, 1]", "output_interval": "(-inf, 0]", "statement": "source (-inf, a + b h + kappa m] = (-inf, 1] 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 5c53cbcbae4adba34b89870e615f520b8a72f52354d065673f12367f986f9d46, 1,999 bytes (854 compressed); download JSON

Cited by

• n-d5fb64ec7bd8ef70 (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