Proof step
Ray basis map theorem
Image under a basis map u^k -> P_k A008277
- Concludes
- Triangle read by rows: 2-Stirling numbers of the second kind.
- Premises
- shift_x_plus_one of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downwar…
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- shift_x_plus_one of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downwar…
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-542308284509574a· 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-2560c863472dcc7b280b1b55d8bf86c1adc63b671f50c194b84a5ae169c736c0f53, 7,525 bytes (1,488 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-6aaec68d653cbdb0(one_signed_coefficients)n-6aaec68d653cbdb0(hadamard_kernel)n-6aaec68d653cbdb0(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