Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013609 of hadamard_factor parent of Triangle read by rows: t(n,m) = binomial(2*n,2*m) * binomial(n,m).
- Premises
- hadamard_factor parent of Triangle read by rows: t(n,m) = binomial(2*n,2*m) * binomial(n,m).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- hadamard_factor parent of Triangle read by rows: t(n,m) = binomial(2*n,2*m) * binomial(n,m).
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-42bba86233fadd35· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "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-2561b3e9b7beb919c19cb9e30f7b6c1050c6bc88f25b1141a58166048be003c4499, 13,875 bytes (2,654 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-1e01398e35510f54(real_rooted)n-1e01398e35510f54(one_signed_coefficients)n-1e01398e35510f54(hadamard_kernel)n-1e01398e35510f54(interlacing)