{"id":"e-721ac318b8b61be8","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-d0afb680af3346da","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":"b6ade9896878aa258d077ed69b9794508207ec3c7a95ba8ed09d4d353982e5f3","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15266,"certificate_compressed_size":2980,"conclusion_name":"basis_map_A013610 of Triangle read by rows: T(n,k) is the number of induced subgraphs of the Lucas cube Lambda(n) that are isomorphic to the hypercube Q(k).","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-299efe8218728fe3","role":"sequence","name":"Triangle read by rows: T(n,k) is the number of induced subgraphs of the Lucas cube Lambda(n) that are isomorphic to the hypercube Q(k).","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-d0afb680af3346da","claim":"real_rooted"},{"node_id":"n-d0afb680af3346da","claim":"one_signed_coefficients"},{"node_id":"n-d0afb680af3346da","claim":"hadamard_kernel"},{"node_id":"n-d0afb680af3346da","claim":"interlacing"}]}