Topology Atlas | Conferences

Knots in Washington XXXVI
May 3-5, 2013
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Catalan States of Generalized Crossings
by
Changsong Li
Department of Mathematical Science, University of Texas at Dallas
Coauthors: Mieczyslaw Dabkowski (UTD) & Jozef Przytycki (GWU)

The main motivation for this work is a problem of finding a closed formula for the product in the Kauffman Bracket Skein Algebra of I-boundle over 3 punctured disk. However, the presentation for this algebra was found by D. Bullock and J. Przytycki and special cases of the formula for product are maybe not hard to find, but finding an explicit general formula for product is still an open problem which leads to many interesting questions. One of them is the problem of finding Kauffman Bracket for a (n+m)-tangle D(m, n) with m horizontal parallel arcs placed over n parallel vertical parallel arcs. In this talk, we will present results of our joint work with M. Dabkowski and J. Przytycki which show that the horizontally excluded Kauffman states for D(m, n) have a description in terms of lattice paths and their number Th(m, n) can be found.

Date received: April 28, 2013

Copyright © 2013 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbhe-11.