Real-rooted atlas

Proof step

Ray basis map theorem

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

Concludes
basis_map_A008277 of derivative of Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by the n-th Catalan number (A000108).
Premises
Theorem
[MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-bd750807e2867e03 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A008277",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
basis_map, SHA-256 f20353ed493b0ecef0d24e72451a0b8f02bf5e6219d89004bd6d1daea3a1ea0a, 14,012 bytes (2,530 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