Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- Triangular array: the fusion of polynomial sequences P and Q given by p(n,x) = (x+2)^n and q(n,x) = (2*x+1)^n.
- Premises
- Triangular matrix arising in enumeration of catafusenes, read by rows.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangular matrix arising in enumeration of catafusenes, read by rows.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-bc7c2cf81eba631a· 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": 2, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-25667eb6bee3ae2027da3dee1b6c84d57427fe938edbd12f6674dc9610dc03b1aab, 10,663 bytes (2,344 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-e5e648370a9e4459(one_signed_coefficients)n-e5e648370a9e4459(hadamard_kernel)n-e5e648370a9e4459(real_rooted)n-e5e648370a9e4459(interlacing)