Proof step
Ray basis map theorem
Image under a basis map u^k -> P_k A008277
- Concludes
- basis_map_A008277 of basis_map_A007318 of Triangle, read by rows of 2*n+1 terms, where row n lists the coefficients in (1+3*x+2*x^2)^n.
- Premises
- basis_map_A007318 of Triangle, read by rows of 2*n+1 terms, where row n lists the coefficients in (1+3*x+2*x^2)^n.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A007318 of Triangle, read by rows of 2*n+1 terms, where row n lists the coefficients in (1+3*x+2*x^2)^n.
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-0bba8026a8691b66· 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-2567975e8c92d8301a7efc4308bc6f5b20f0dfe913ab20c9c5288eba1fb082dda21, 7,715 bytes (1,527 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-29feaac19fa9e41e(real_rooted)n-29feaac19fa9e41e(one_signed_coefficients)n-29feaac19fa9e41e(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