Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013610
- Concludes
- derivative of Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*3^j.
- Premises
- derivative of Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n >= 1, 0 <= k <= n-1). A level is …
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- derivative of Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n >= 1, 0 <= k <= n-1). A level is …
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-6521fdb104380f39· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013610", "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-2568109c7ecec220a856a12d6d6753f8d2018fba3fab4cf8fd1f96197fb239a3148, 15,239 bytes (2,814 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-1d7b3a8d2533ff46(real_rooted)n-1d7b3a8d2533ff46(one_signed_coefficients)n-1d7b3a8d2533ff46(hadamard_kernel)n-1d7b3a8d2533ff46(interlacing)