Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- shift_x_plus_one 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-2f8cdcb49ab0e57e· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "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-2567fbb7f2c295be654237b6a206ed91f8501d6132ce1a300708ea29a53b5609848, 14,346 bytes (2,678 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-2caa837a4ea68fa4(one_signed_coefficients)n-2caa837a4ea68fa4(hadamard_kernel)n-2caa837a4ea68fa4(interlacing)n-2caa837a4ea68fa4(real_rooted)