Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
- 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-5cc57d6c555931a3· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "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-256f11d70430f2726c4263752d0f7992fada8201ff0f00353edf36f431a6723affc, 14,417 bytes (2,792 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-392f49b496f79fbf(real_rooted)n-392f49b496f79fbf(one_signed_coefficients)n-392f49b496f79fbf(hadamard_kernel)n-392f49b496f79fbf(interlacing)