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CMFD, 2013, Volume 51, Pages 87–109 (Mi cmfd256)  

On the combinatorics of smoothing

M. W. Chrisman

Department of Mathematics, Monmouth University, West Long Branch, NJ, USA

Abstract: 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.

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English version:
Journal of Mathematical Sciences, 2016, 214:5, 609–631

UDC: 515.162.8

Citation: M. W. Chrisman, “On the combinatorics of smoothing”, Topology, CMFD, 51, PFUR, M., 2013, 87–109; Journal of Mathematical Sciences, 214:5 (2016), 609–631

Citation in format AMSBIB
\Bibitem{Chr13}
\by M.~W.~Chrisman
\paper On the combinatorics of smoothing
\inbook Topology
\serial CMFD
\yr 2013
\vol 51
\pages 87--109
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd256}
\transl
\jour Journal of Mathematical Sciences
\yr 2016
\vol 214
\issue 5
\pages 609--631
\crossref{https://doi.org/10.1007/s10958-016-2802-5}


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