Real-rooted atlas

Proof step

Ray basis map theorem

Image under a basis map u^k -> P_k A008277

Concludes
basis_map_A008277 of Triangle read by rows: T(n, k) = binomial(n, k) if n < 3, otherwise T(n, k) = binomial(n, k) + 2*binomial(n-2, k-1).
Premises
Theorem
[MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-0104d750fd8745b9 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A008277",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
basis_map, SHA-256 1e844e6e48340e0cde6eb56b4a194f939dd996bf83d4a1137adb8f4690808681, 9,647 bytes (2,025 compressed); download
polytool replayed the certificate when the step was written.
Cited by

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