Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- shift_x_plus_one of basis_map_A013611 of Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n).
- Premises
- basis_map_A013609 of Triangular array read by rows: 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]
- basis_map_A013609 of Triangular array read by rows: 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-4061325ce955aa51· 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-2565c24b3bdfc62be46201d04d2fabe3c61d8731e665e1739a0a75c4f59b465c855, 14,852 bytes (2,964 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-e88e218539d1c5b8(interlacing)n-e88e218539d1c5b8(one_signed_coefficients)n-e88e218539d1c5b8(hadamard_kernel)n-e88e218539d1c5b8(real_rooted)