Catalan States of Lattice Crossing
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 Catala...
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| Veröffentlicht in: | arXiv.org 2014-09 |
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| creator | Dabkowski, Mieczyslaw K Li, Changsong Przytycki, Jozef H |
| description | 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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| title | Catalan States of Lattice Crossing |
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