Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Induction on Descent in Leaper Graphs   We construct an infinite ternary tree $\mathfrak{L}$ whose root is the knight
and whose vertices are all skew free leapers. We define the descent of a skew
free leaper to be its "address" within $\mathfrak{L}$. We introduce three
transformations which relate the leaper graphs of a skew free leaper to the
leaper graphs of its three children in $\mathfrak{L}$. By starting with the
knight and then applying these transformations so as to advance throughout
$\mathfrak{L}$, we can establish theorems about all skew free leapers. We call
this proof technique induction on descent and with its help we resolve a number
of questions about leaper graphs.

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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin