Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Set Matching: An Enhancement of the Hales-Jewett Pairing Strategy   When solving k-in-a-Row games, the Hales-Jewett pairing strategy [4] is a
well-known strategy to prove that specific positions are (at most) a draw. It
requires two empty squares per possible winning line (group) to be marked,
i.e., with a coverage ratio of 2.0. In this paper we present a new strategy,
called Set Matching. A matching set consists of a set of nodes (the markers), a
set of possible winning lines (the groups), and a coverage set indicating how
all groups are covered after every first initial move. This strategy needs less
than two markers per group. As such it is able to prove positions in k-in-a-Row
games to be draws, which cannot be proven using the Hales-Jewett pairing
strategy. We show several efficient configurations with their matching sets.
These include Cycle Configurations, BiCycle Configurations, and PolyCycle
Configurations involving more than two cycles. Depending on configuration, the
coverage ratio can be reduced to 1.14. Many examples in the domain of solving
k-in-a-Row games are given, including the direct proof (without further
investigation) that the empty 4 x 4 board is a draw for 4-in-a-Row.

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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol