Proof step
Ray basis map theorem
Image under a basis map u^k -> P_k A008277
- Concludes
- basis_map_A008277 of Triangular array: the fusion of (x+1)^n and (x+2)^n; see Comments for the definition of fusion.
- Premises
- Triangular array: the fusion of (x+1)^n and (x+2)^n; see Comments for the definition of fusion.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangular array: the fusion of (x+1)^n and (x+2)^n; see Comments for the definition of fusion.
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-a46a1743d9a33bd5· 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-2562f8d462bbdebaa45417a018575f141e6ef313fe1e979a7c7d1d56ca8ddf02a07, 9,483 bytes (2,014 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-25f220f6ac2768f4(real_rooted)n-25f220f6ac2768f4(one_signed_coefficients)n-25f220f6ac2768f4(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