Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013610
- Concludes
- basis_map_A013610 of theta_plus_one_squared of Triangle read by rows: row n consists of n zeros followed by n!.
- Premises
- theta_plus_one_squared 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]
- theta_plus_one_squared 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-5c3418536cf58ed4· 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-256d69cc457360338a120fba465be5af9735c9a9bab8382b248481085d8b432bdd4, 14,816 bytes (2,762 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-43eaa6e83c4da2ce(real_rooted)n-43eaa6e83c4da2ce(one_signed_coefficients)n-43eaa6e83c4da2ce(hadamard_kernel)n-43eaa6e83c4da2ce(interlacing)