Proof step
Ray basis map theorem
Image under a basis map u^k -> P_k A008277
- Concludes
- basis_map_A008277 of basis_map_A013609 of Triangle of coefficients in expansion of (1+3*x)^n.
- Premises
- basis_map_A013609 of Triangle of coefficients in expansion of (1+3*x)^n.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013609 of Triangle of coefficients in expansion of (1+3*x)^n.
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-73339d7dd53f84c4· 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-2568e93834ad0a0eda82549c11fee4b5b85773308b6d00d4dcb089daf6cef9c8c2d, 7,527 bytes (1,504 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-fb4d4dfa4db08258(one_signed_coefficients)n-fb4d4dfa4db08258(hadamard_kernel)n-fb4d4dfa4db08258(real_rooted)
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