Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013609 of basis_map_A013609 of Triangle read by rows: row n consists of n zeros followed by n!.
- Premises
- basis_map_A013609 of Triangle read by rows: row n consists of n zeros followed by n!.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013609 of Triangle read by rows: row n consists of n zeros followed by n!.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-c2ad40d92b85133c· 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-256e1b891f60b755874b37bc655e9d23d6271cdf7c5c4d51e5bf6f7938322fec89d, 10,244 bytes (2,286 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-a995131b65a4af0c(one_signed_coefficients)n-a995131b65a4af0c(hadamard_kernel)n-a995131b65a4af0c(interlacing)n-a995131b65a4af0c(real_rooted)