Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A038207
- Concludes
- 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
- basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 1]
- basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-021cb85ecd05303e· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A038207", "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-256d84058bc2f59a0070aa7e623adfc82e077766b34430bc75aa7b42c761dc4ef29, 14,417 bytes (2,798 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-c72653d9ab0ee8be(one_signed_coefficients)n-c72653d9ab0ee8be(hadamard_kernel)n-c72653d9ab0ee8be(real_rooted)n-c72653d9ab0ee8be(interlacing)