We give an algorithmic computation for the height of Kauffman's clock lattice obtained from a knot diagram with two adjacent regions starred and without crossing information specified. We show that this lattice is more familiarly the graph of perfect matchings of a bipartite graph obtained from the knot diagram by overlaying the two dual Tait graphs of the knot diagram. Furthermore we prove structural properties of the bipartite graph in general. This setting also makes evident applications to Chebyshev or harmonic knots, whose related bipartite graph is the popular grid graph, and to discrete Morse functions.
@article{10_37236_3395,
author = {Moshe Cohen and Mina Teicher},
title = {Kauffman's clock lattice as a graph of perfect matchings: a formula for its height},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {4},
doi = {10.37236/3395},
zbl = {1302.57017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3395/}
}
TY - JOUR
AU - Moshe Cohen
AU - Mina Teicher
TI - Kauffman's clock lattice as a graph of perfect matchings: a formula for its height
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/3395/
DO - 10.37236/3395
ID - 10_37236_3395
ER -
%0 Journal Article
%A Moshe Cohen
%A Mina Teicher
%T Kauffman's clock lattice as a graph of perfect matchings: a formula for its height
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/3395/
%R 10.37236/3395
%F 10_37236_3395
Moshe Cohen; Mina Teicher. Kauffman's clock lattice as a graph of perfect matchings: a formula for its height. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/3395
