p-Colorings of Weaving Knots

نویسنده

  • Layla Oesper
چکیده

We explore the p-colorability of a family of knots known as weaving knots. First, we show some general results pertaining to p-coloring any (m, n) weaving knot. We then determine the p-colorability of any (m, 3) weaving knot, and designate these p-colorings into two separate types, whose characteristics we begin to explore. We also partially classify some of the p-colorings for any (m, n) weaving knot when n is even. Finally, we discuss different ways to count the number of p-colorings of a knot and then use these counting methods to calculate the number of one type of p-coloring of (m, 3) weaving knots.

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تاریخ انتشار 2005