Proof step e-e9721368474f6fa1

basis_map_theorem → concludes about Galton triangle T(n, k) = T(n-1, k-1) + (3k-2)*T(n-1, k) read by rows. 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 4393f824ac43e21ead16385d44c16ae4b1c37c47abf3836e7ff345260b5918b6, 1,991 bytes (841 compressed); download JSON

Cited by

• n-cab14672969f6507 (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