Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013611
- Concludes
- basis_map_A013611 of basis-map coefficients of Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)}…
- Premises
- basis-map coefficients of Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)} …
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis-map coefficients of Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)} …
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-422c7a2dd7cada12· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013611", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-2561747f064208e71350277d5cf21adaf9c1eb15ea769c05a2ea744c5a2655d6996, 7,661 bytes (1,707 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-1a01d480c8d600c3(real_rooted)n-1a01d480c8d600c3(one_signed_coefficients)n-1a01d480c8d600c3(hadamard_kernel)