Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Game Theory, Well-Tempered Scoring Games, and a Knot Game   We begin by reviewing and proving the basic facts of combinatorial game
theory. We then consider scoring games (also known as Milnor games or
positional games), focusing on the "fixed-length" games for which all sequences
of play terminate after the same number of moves. The theory of fixed-length
scoring games is shown to have properties similar to the theory of loopy
combinatorial games, with operations similar to onsides and offsides. We give a
complete description of the structure of fixed-length scoring games in terms of
the class of short partizan games. We also consider fixed-length scoring games
taking values in the two-element boolean algebra, and classify these games up
to indistinguishability. We then apply these results to analyze some positions
in the knotting-unknotting game of Pechenik, Townsend, Henrich, MacNaughton,
and Silversmith.

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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int