Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013610
- Concludes
- basis_map_A013610 of One half of odd-numbered entries of even-numbered rows of Pascal's triangle A007318.
- Premises
- One half of odd-numbered entries of even-numbered rows of Pascal's triangle A007318.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- One half of odd-numbered entries of even-numbered rows of Pascal's triangle A007318.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-fbf96dcf4edeca17· 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": 1, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-25677f831c010e470321f0c982043c06e23473e6453cbfe232c5184378b86c98ab1, 13,769 bytes (2,620 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-08fe62d9c34c34e9(real_rooted)n-08fe62d9c34c34e9(one_signed_coefficients)n-08fe62d9c34c34e9(hadamard_kernel)n-08fe62d9c34c34e9(interlacing)