Carric mat and the further research on bipartite knots

The existence of non-bipartite knot was conjectured in 1987 by Przytycki and proven by Duzhin in 2011. We disprove the conjecture that bipartite knots should have the trivial second Alexander ideal. We construct a family inside the class of bipartite knots that contains all rational knots and has the trivial second Alexander ideal. We present a matched diagram of the knot [Formula: see text]. Also we demonstrate a combinatorial techniques that could be useful for further research on bipartite knots.