Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013611
- Concludes
- basis_map_A013611 of Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + j*prime(j)*T(n-2, k-1) with j=3, read by rows.
- Premises
- Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + j*prime(j)*T(n-2, k-1) with j=3, read by rows.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + j*prime(j)*T(n-2, k-1) with j=3, read by rows.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-cf37d259e4a0d2e0· 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-256b9786f5727465785eb5b9a690346ce03d637472decd536c05c65e901ef69b882, 14,637 bytes (2,796 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-e1680309668a7c43(real_rooted)n-e1680309668a7c43(one_signed_coefficients)n-e1680309668a7c43(hadamard_kernel)n-e1680309668a7c43(interlacing)