Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Martin Gardner Polytopes   In the chapter "Magic with a Matrix" in \emph{Hexaflexagons and Other
Mathematical Diversions} (1988), Martin Gardner describes a delightful "party
trick" to fill the squares of a $d$-by-$d$ chessboard with nonnegative integers
such that the sum of the numbers covered by any placement of $d$ nonthreatening
rooks is a given number $N$. We consider such chessboards from a geometric
perspective which gives rise to a family of lattice polytopes. The polyhedral
structure of these Gardner polytopes explains the underlying trick and enables
us to count such chessboards for given $N$ in three different ways. We also
observe a curious duality that relates Gardner polytopes to Birkhoff polytopes.

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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph