Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- derivative of Triangle whose (i,j)-th entry is binomial(i,j)*2^i.
- Premises
- derivative of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- derivative of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the…
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-7f20be522e7ff097· 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" } } }{ "claim": "interlacing", "from_index": 2, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-256713a4e63fc315e55bb75f42330d9edd9144ca0fa72ad3975197b1cef348da3e0, 15,385 bytes (2,864 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-2494c903d5dafb67(real_rooted)n-2494c903d5dafb67(one_signed_coefficients)n-2494c903d5dafb67(hadamard_kernel)n-2494c903d5dafb67(interlacing)