Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- basis_map_A013611 of Triangle whose (i,j)-th entry is 5^(i-j)*binomial(i,j).
- Premises
- basis_map_A013609 of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013609 of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed…
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-d630419ad374791a· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-25668eaa63e3bac6866850f22c8275ac32aa4c50f59abdf46781047e2a0ee3fdef9, 6,855 bytes (1,388 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-408f7506d6594551(real_rooted)n-408f7506d6594551(one_signed_coefficients)n-408f7506d6594551(hadamard_kernel)