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arXiv · 1409.4065

Catalan States of Lattice Crossing

Mieczyslaw K. Dabkowski·Changsong Li·Jozef H. Przytycki
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Abstract

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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BibTeXRIS

Mieczyslaw K. Dabkowski, Changsong Li, Jozef H. Przytycki. 2014-09-14. Catalan States of Lattice Crossing. https://arxiv.org/abs/1409.4065

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