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, (n-1) zeros followed by 2^n - 1.
- Premises
- Triangle read by rows, (n-1) zeros followed by 2^n - 1.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows, (n-1) zeros followed by 2^n - 1.
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-002b84ccf8b2daff· 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-256300f7ccc9a62eb62f4f12c90d0fbd9493fca59702394c758887c9fa2b5f39efc, 13,275 bytes (2,435 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-b847f956136e2433(real_rooted)n-b847f956136e2433(one_signed_coefficients)n-b847f956136e2433(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