Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- shift_x_plus_one of 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…
- 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
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-50df82299b1ca0f4· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-25693d5bf81099163bd4ea8744234753ab98ecf1e461f0f1b426ca718f594dc8c08, 6,855 bytes (1,382 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-9d1e54ec2606728d(one_signed_coefficients)n-9d1e54ec2606728d(hadamard_kernel)n-9d1e54ec2606728d(real_rooted)