Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- shift_x_plus_one of basis_map_A007318 of Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.
- Premises
- basis_map_A007318 of Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A007318 of Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-2ac4bb385554061c· 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-2569c5f971cb0b02fe518f0a041b8107dda108396d1c1013d385cfdef643a68aa01, 10,252 bytes (2,284 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-26a40306b1f4a278(one_signed_coefficients)n-26a40306b1f4a278(hadamard_kernel)n-26a40306b1f4a278(interlacing)n-26a40306b1f4a278(real_rooted)