Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
- Premises
- basis-map coefficients of Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 1]
- basis-map coefficients of Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-c670888797b52216· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "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-25610a005214e8cfb484c5b664518c69493dcf5e71193abf59eae5164fbd7b7a96c, 15,253 bytes (2,835 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-511a2225fa2191c9(real_rooted)n-511a2225fa2191c9(one_signed_coefficients)n-511a2225fa2191c9(hadamard_kernel)n-511a2225fa2191c9(interlacing)