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Carric mat and the further research on bipartite knots
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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.
Title: Carric mat and the further research on bipartite knots
Description:
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.
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