Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013610
- Concludes
- basis_map_A013610 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-e2ffdfe4fa2ea96c· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013610", "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-25699004de7249b311b0d59d0069b940b3907dff105a3e6db24896f3d10d284dc14, 14,334 bytes (2,823 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-0644de73021829bb(real_rooted)n-0644de73021829bb(one_signed_coefficients)n-0644de73021829bb(hadamard_kernel)n-0644de73021829bb(interlacing)