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,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1.
- Premises
- Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-908cf64d7804d7c8· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013611", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }{ "claim": "interlacing", "from_index": 2, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-25647308588e2b2f372738b1a3f49c9024c1f3a5bb0693d0a5d5b99e793b191221e, 14,819 bytes (2,894 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-2156f740e0c97180(real_rooted)n-2156f740e0c97180(one_signed_coefficients)n-2156f740e0c97180(hadamard_kernel)n-2156f740e0c97180(interlacing)