Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013609 of shift_x_plus_one of Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).
- Premises
- shift_x_plus_one of Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- shift_x_plus_one of Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-58c7c138b5508493· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }{ "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-2568bb6c1951d1dadfd86bcf16c17f0d60adabe123cbc954e46169efa886fb159ef, 14,346 bytes (2,684 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-31a1b9b1779ea532(real_rooted)n-31a1b9b1779ea532(one_signed_coefficients)n-31a1b9b1779ea532(hadamard_kernel)n-31a1b9b1779ea532(interlacing)