Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving Infinite Kolam in Knot Theory   In south India, there are traditional patterns of line-drawings encircling
dots, called ``Kolam'', among which one-line drawings or the ``infinite Kolam''
provide very interesting questions in mathematics. For example, we address the
following simple question: how many patterns of infinite Kolam can we draw for
a given grid pattern of dots? The simplest way is to draw possible patterns of
Kolam while judging if it is infinite Kolam. Such a search problem seems to be
NP complete. However, it is certainly not. In this paper, we focus on
diamond-shaped grid patterns of dots, (1-3-5-3-1) and (1-3-5-7-5-3-1) in
particular. By using the knot-theory description of the infinite Kolam, we show
how to find the solution, which inevitably gives a sketch of the proof for the
statement ``infinite Kolam is not NP complete.'' Its further discussion will be
given in the final section.

27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat