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 in which T(n,k) is the number of length k chains from (0,0) to (n,n) of the poset [n] X [n] ordered by the product o…
Premises
Theorem
[MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-14e4fe32a6cd6e38 · 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 ddd439d40dfb8acf7a6f449a043a836a199af16830fee1548e9c4292bebe6081, 13,769 bytes (2,375 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