Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The switch operators and push-the-button games: a sequential compound
  over rulesets   We study operators that combine combinatorial games. This field was initiated
by Sprague-Grundy (1930s), Milnor (1950s) and Berlekamp-Conway-Guy (1970-80s)
via the now classical disjunctive sum operator on (abstract) games. The new
class consists in operators for rulesets, dubbed the switch-operators. The
ordered pair of rulesets (R 1 , R 2) is compatible if, given any position in R
1 , there is a description of how to move in R 2. Given compatible (R 1 , R 2),
we build the push-the-button game R 1 R 2 , where players start by playing
according to the rules R 1 , but at some point during play, one of the players
must switch the rules to R 2 , by pushing the button ". Thus, the game ends
according to the terminal condition of ruleset R 2. We study the pairwise
combinations of the classical rulesets Nim, Wythoff and Euclid. In addition, we
prove that standard periodicity results for Subtraction games transfer to this
setting, and we give partial results for a variation of Domineering, where R 1
is the game where the players put the domino tiles horizontally and R 2 the
game where they play vertically (thus generalizing the octal game 0.07).

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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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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: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph