TY - JOUR
T1 - Kauffman’s clock lattice as a graph of perfect matchings
T2 - A formula for its height
AU - Cohen, Moshe
AU - Teicher, Mina
N1 - Publisher Copyright:
© 2014, Australian National University. All rights reserved.
PY - 2014/11/13
Y1 - 2014/11/13
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84938684293&partnerID=8YFLogxK
U2 - 10.37236/3395
DO - 10.37236/3395
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SN - 1077-8926
VL - 21
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 4
M1 - P4.31
ER -