Proof step e-4720724f7f8010a1

basis_map_theorem → concludes about Triangular array a(n,k) = (1/k)*Sum_{i=0..k} (-1)^(k-i)*binomial(k,i)*i^n; n >= 1, 1 <= k <= n, read by rows. 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": "[0, 1]", "output_interval": "[-1, 0]", "statement": "source [0, 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 a2ca64371a271524183852f9e53dc239f35178b10ce2f32bc3a70089fffe4627, 2,494 bytes (973 compressed); download JSON

Cited by

• n-677d34c7af372519 (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