7 research outputs found
Grid graphs, Gorenstein polytopes, and domino stackings
We examine domino tilings of rectangular boards, which are in natural
bijection with perfect matchings of grid graphs. This leads to the study of
their associated perfect matching polytopes, and we present some of their
properties, in particular, when these polytopes are Gorenstein. We also
introduce the notion of domino stackings and present some results and several
open questions. Our techniques use results from graph theory, polyhedral
geometry, and enumerative combinatorics.Comment: 14 pages, 6 figures, uses graphs packag
The Jones polynomials of 3-bridge knots via Chebyshev knots and billiard table diagrams
This work presents formulas for the Kauffman bracket and Jones polynomials of
3-bridge knots using the structure of Chebyshev knots and their billiard table
diagrams. In particular, these give far fewer terms than in the Skein relation
expansion. The subject is introduced by considering the easier case of 2-bridge
knots, where some geometric interpretation is provided, as well, via
combinatorial tiling problems.Comment: 20 pages, 4 figures, 2 table