Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013609 of Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
- Premises
- Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-6f31f52cec5634fa· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }{ "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-256b5fc3381508f1a0a3fcf1f6c1b5ee8724232b6f7339ab2a56909f775d7239741, 14,334 bytes (2,824 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-726576b543a7afe5(real_rooted)n-726576b543a7afe5(one_signed_coefficients)n-726576b543a7afe5(hadamard_kernel)n-726576b543a7afe5(interlacing)