Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- shift_x_plus_one of gamma_polynomial of Pascal-(1,6,1) array.
- Premises
- basis_map_A007318 of Triangle T(n,k) = T(n-1,k) + 3*T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1, T(n,k) = 0 for n or k < 0, read by r…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A007318 of Triangle T(n,k) = T(n-1,k) + 3*T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1, T(n,k) = 0 for n or k < 0, read by r…
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-30a39ecb8a3fcb98· 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-256f763ba3451c6da8f7dd7a1a16500d00fac777c7c5de5141a238981acfbd298bb, 14,963 bytes (3,009 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-3f9fff45963528a2(one_signed_coefficients)n-3f9fff45963528a2(hadamard_kernel)n-3f9fff45963528a2(real_rooted)n-3f9fff45963528a2(interlacing)