Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013611
- Concludes
- basis_map_A013611 of Triangle read by rows: T(n,0)=1, T(n,n)=2, T(n,m) = T(n-1,m-1) + Sum_{k=0..m} T(n-1-k,m-k).
- Premises
- Triangle read by rows: T(n,0)=1, T(n,n)=2, T(n,m) = T(n-1,m-1) + Sum_{k=0..m} T(n-1-k,m-k).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows: T(n,0)=1, T(n,n)=2, T(n,m) = T(n-1,m-1) + Sum_{k=0..m} T(n-1-k,m-k).
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-558ac76b5d434951· 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" } } }{ "claim": "interlacing", "from_index": 2, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-2562275b4279d82b7393a3cbf93a7464a79bb8f7e339cf5d6338882bae28da081e2, 14,210 bytes (2,667 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-8018092894e25502(real_rooted)n-8018092894e25502(one_signed_coefficients)n-8018092894e25502(hadamard_kernel)n-8018092894e25502(interlacing)