格点相交的Catalan态
Catalan States of Lattice Crossing
摘要：
对于格点交叉$L\left( m,n\right) $，我们证明了在$m\times n$矩形$P$边界上的$2\left( m+n\right) $点之间的哪种Catalan连接可以实现为Kauffman态，并给出了这种Catalan连接的数目的显式公式.对于Catalan联络，如果没有弧起始和终止在缠结的同一侧，我们在$P\times I$的相对Kauffman Kauffman Skein模中找到了其系数的闭公式
英文摘要：
For a Lattice crossing $L\left( m,n\right) $ we show which Catalan connection between $2\left( m+n\right) $ points on boundary of $m\times n$ rectangle $P$ can be realized as a Kauffman state and we give an explicit formula for the number of such Catalan connections. For the case of a Catalan connection with no arc starting and ending on the same side of the tangle, we find a closed formula for its coefficient in the Relative Kauffman Bracket Skein Module of $P\times I$
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