Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013609 of basis_map_A013611 of Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirlin…
- Premises
- basis_map_A013611 of Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013611 of Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling…
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-2eb001b4ddb2fe60· 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" } } }{ "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-2567dc38e813726fe5fedcd4bde6afa156e5f1129e5320aba1780270504770a1921, 10,255 bytes (2,296 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-433851efa70ad8d5(real_rooted)n-433851efa70ad8d5(one_signed_coefficients)n-433851efa70ad8d5(hadamard_kernel)n-433851efa70ad8d5(interlacing)