Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A $q$-Queens Problem. IV. Attacking Configurations and Their
  Denominators   In Parts I-III we showed that the number of ways to place $q$ nonattacking
queens or similar chess pieces on an $n\times n$ chessboard is a
quasipolynomial function of $n$ whose coefficients are essentially polynomials
in $q$.
  In this part we focus on the periods of those quasipolynomials. We calculate
denominators of vertices of the inside-out polytope, since the period is
bounded by, and conjecturally equal to, their least common denominator. We find
an exact formula for that denominator of every piece with one move and of
two-move pieces having a horizontal move. For pieces with three or more moves,
we produce geometrical constructions related to the Fibonacci numbers that show
the denominator grows at least exponentially with $q$.

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The categories of this paper are: ao-sci
16
The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
3
The categories of this paper are: physics