Geodesic
On the combinatorics of smoothing
Contemporary Mathematics. Fundamental Directions, Topology, Tome 51 (2013), pp. 87-109

Voir la notice de l'article provenant de la source Math-Net.Ru

Many invariants of knots rely upon smoothing the knot at its crossings. To compute them, it is necessary to know how to count the number of connected components the knot diagram is broken into after the smoothing. In this paper, it is shown how to use a modification of a theorem of Zulli together with a modification of the spectral theory of graphs to approach such problems systematically. We give an application to counting subdiagrams of pretzel knots which have one component after oriented and unoriented smoothings. 
@article{CMFD_2013_51_a5,
     author = {M. W. Chrisman},
     title = {On the combinatorics of smoothing},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {87--109},
     publisher = {mathdoc},
     volume = {51},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2013_51_a5/}
}
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M. W. Chrisman. On the combinatorics of smoothing. Contemporary Mathematics. Fundamental Directions, Topology, Tome 51 (2013), pp. 87-109. http://geodesic.mathdoc.fr/item/CMFD_2013_51_a5/