In 2008, Kauffman and Lomonaco introduced the concepts
of a knot mosaic and the mosaic number of a knot or link
, the smallest
integer
such that
can be represented
on an
-mosaic.
In 2018, the authors of this paper introduced and explored space-efficient knot mosaics and the
tile number of
,
the smallest number of nonblank tiles necessary to depict
on a
knot mosaic. They determine bounds for the tile number in terms of the mosaic
number. In this paper, we focus specifically on prime knots with mosaic number 6.
We determine a complete list of these knots, provide a minimal, space-efficient knot
mosaic for each of them, and determine the tile number (or minimal mosaic tile
number) of each of them.
