Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling1 triangle.
- 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-e0cc3c6bcdba4635· 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" } } }- Certificate
basis_map, SHA-256cdf11f6bd17ef54d59df148859469acc84701f3889c7f9a5325147680bf504ff, 7,661 bytes (1,703 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-260e022530e5976c(one_signed_coefficients)n-260e022530e5976c(hadamard_kernel)n-260e022530e5976c(real_rooted)