{"id":"e-be796d1c3c5c0ab8","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-97b51734d39ede6c","premise_count":0,"theorem":"L. L. Liu and Y. Wang, Adv. Appl. Math. 38 (2007) 542-560, Theorem 2.1 and Corollary 2.4 (A unified approach to polynomial sequences with only real zeros; the lag row as the interlacer, b_n = 0), weak interlacing of consecutive rows, with nonnegativity of the coefficients replaced, where a root region is certified, by an exact root-location induction","lean_route":null,"lean_declarations":["RealRooted.MaWang.strictInterl_of_interlaces_evalCoeff_nonpos"],"certificate_hash":"5911714ecaf0cf0767034500569708a428d55bf4f92bf4fb367870a105e55762","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":5004,"certificate_compressed_size":1416,"conclusion_name":"Triangle of Bessel numbers read by rows: T(n,k) is the number of k-matchings of the complete graph K(n).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":false,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-97b51734d39ede6c","claim":"one_signed_coefficients"},{"node_id":"n-97b51734d39ede6c","claim":"hadamard_kernel"},{"node_id":"n-97b51734d39ede6c","claim":"interlacing"},{"node_id":"n-97b51734d39ede6c","claim":"real_rooted"}]}
