Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- basis_map_A007318 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-3f6a1f9b0dbed70e· 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": 1, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-25685370d2219be191bd953dfce3760a955668ee40cc05b44b372f4bd2eda5d0ce0, 14,146 bytes (2,730 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-216193c52744946f(interlacing)n-216193c52744946f(real_rooted)n-216193c52744946f(one_signed_coefficients)n-216193c52744946f(hadamard_kernel)