Intersection numbers of bipartite distance-regular graphs

Let l denote a bipartite distance-regular graph with diameter d⩾2, and intersection numbers 1=c1,c2,…,cd=k. For any integer i(1⩽i⩽d−1), we find a collection of lower bounds for the quantity ci+1−1−ci(μ−1) where μ:=c2. Our results imply that if kci((μ−1)(μ−2)(ci−ci−1−1)2+1) then ci+1⩾ci(μ−1)+1.