Proof step
Ray basis map theorem
Image under a basis map u^k -> P_k A008277
- Concludes
- basis_map_A008277 of Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
- Premises
- Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-e5b9ba028840ff44· 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-256d97244f4073ecff0caff3edede6e21972f7215305ab9186df772069e0a733fde, 13,039 bytes (2,484 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-acced3d80d92e3dd(real_rooted)n-acced3d80d92e3dd(one_signed_coefficients)n-acced3d80d92e3dd(hadamard_kernel)
References
- [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