Flip Graphs on Self-Complementary Ideals of Chain Products

In this paper, we introduce a flip operation on self-complementary ideals ofchain product posets and study the resulting flip graphs. We give asymptoticsfor the number of vertices in these graphs, compute their diameters, and givebounds for their radii. We also define similar flip operations onself-complementary ideals of the chain product $[2r]\times [2r]\times [2r]$satisfying additional symmetries, and we achieve similar results for theresulting flip graphs.