Sequences of Spiral Knot Determinants
Seong Ju Kim, Ryan Stees, and Laura Taalman
Department of Mathematics and Statistics
James Madison University
305 Roop Hall, MSC 1911
Harrisonburg, VA 22807
Spiral knots are a generalization of the well-known class of torus
knots indexed by strand number and base word repetition. By fixing the
strand number and varying the repetition index, we obtain integer
sequences of spiral knot determinants. In this paper, we examine such
sequences for spiral knots of up to four strands using a new periodic
crossing matrix method. Surprisingly, the resulting sequences vary
widely in character and, even more surprisingly, nearly every one of
them is a known integer sequence in the Online Encyclopedia of Integer
Sequences. We also develop a general form for these sequences in terms
of recurrence relations that exhibits a pattern which is potentially
generalizable to all spiral knots.
Full version: pdf,
(Concerned with sequences
Received March 10 2015; revised versions received October 18 2015; November 17 2015.
Published in Journal of Integer Sequences, December 17 2015.
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