Catalan States of Lattice Crossing

Mieczyslaw K. Dabkowski; Changsong Li; Jozef H. Przytycki

Catalan States of Lattice Crossing

Geometric Topology 2014-09-16 v1

Authors: Mieczyslaw K. Dabkowski , Changsong Li , Jozef H. Przytycki

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 $P\times I$

Keywords

Catalan states lattice crossing Kauffman state Relative Kauffman Bracket Skein Module closed formula Catalan connection

Cite

@article{arxiv.1409.4065,
  title  = {Catalan States of Lattice Crossing},
  author = {Mieczyslaw K. Dabkowski and Changsong Li and Jozef H. Przytycki},
  journal= {arXiv preprint arXiv:1409.4065},
  year   = {2014}
}

Comments

12 pages, 18 figures

Catalan States of Lattice Crossing

Abstract

Keywords

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