Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013609 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-f6b768e64ebd4b5e· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-25633994c15f736018daa6399fe71d6928b449643503d010b54ee214e523c71b401, 7,661 bytes (1,708 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-20bccc4c38847de1(real_rooted)n-20bccc4c38847de1(one_signed_coefficients)n-20bccc4c38847de1(hadamard_kernel)