Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- shift_x_plus_one of basis_map_A013609 of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
- Premises
- basis_map_A007318 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.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A007318 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.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-a9ccf5f34daf84e6· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "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-25644287bcc9562f8ce4b4ffd37b6c48d442dd33e6bd2317a77e4c3af40d1942684, 14,967 bytes (2,906 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-40465177841ad1ac(interlacing)n-40465177841ad1ac(one_signed_coefficients)n-40465177841ad1ac(hadamard_kernel)n-40465177841ad1ac(real_rooted)