Proof step
Ray basis map theorem
Image under a basis map u^k -> P_k A008277
- Concludes
- basis_map_A008277 of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator xDx, iterated…
- Premises
- Triangle read by rows: row n consists of n zeros followed by n+1.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows: row n consists of n zeros followed by n+1.
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-d0b2fd1afad7f0a4· 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-256afe6425eee5adcb76a3235c1773b163341909309568babc97974b3e09313a0fe, 13,275 bytes (2,429 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-ebfce87a1d1893bb(real_rooted)n-ebfce87a1d1893bb(one_signed_coefficients)n-ebfce87a1d1893bb(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