{"id":"e-9141b466b4e3524d","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-50746bd627deaa2a","premise_count":1,"theorem":"geometric family P_k = g(t) (a + d t)^k: T(p) = g(t) p(a + d t), so the roots of T(p) are those of g and the points (r - a)/d for the roots r of p (elementary)","lean_route":null,"lean_declarations":[],"certificate_hash":"8e6dad8922d9ff7964c743ac1bbd63d8226bcb5a3b5f8a1741624ad0f2f76d0a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14598,"certificate_compressed_size":2751,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n,k) is the number of k-matchings in the n-sunlet graph (0 <= k <= n).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-9d2e609ab19d361f","role":"sequence","name":"Triangle read by rows: T(n,k) is the number of k-matchings in the n-sunlet graph (0 <= k <= n).","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-50746bd627deaa2a","claim":"one_signed_coefficients"},{"node_id":"n-50746bd627deaa2a","claim":"hadamard_kernel"},{"node_id":"n-50746bd627deaa2a","claim":"interlacing"},{"node_id":"n-50746bd627deaa2a","claim":"real_rooted"}]}