Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- basis_map_A007318 of Triangle of even numbered entries of odd numbered rows of Pascal's triangle A007318.
- Premises
- Triangle of even numbered entries of odd numbered rows of Pascal's triangle A007318.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- Triangle of even numbered entries of odd numbered rows of Pascal's triangle A007318.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-56956d6724ecd488· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }{ "claim": "interlacing", "from_index": 2, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-2562bc4d8706bef662fa1f18df095d4b028689da7f147568c8449053956aad28870, 13,769 bytes (2,620 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-2887a9a5b94917e3(real_rooted)n-2887a9a5b94917e3(one_signed_coefficients)n-2887a9a5b94917e3(hadamard_kernel)n-2887a9a5b94917e3(interlacing)