Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The largest and the smallest fixed points of permutations   We give a new interpretation of the derangement numbers d_n as the sum of the
values of the largest fixed points of all non-derangements of length n-1. We
also show that the analogous sum for the smallest fixed points equals the
number of permutations of length n with at least two fixed points. We provide
analytic and bijective proofs of both results, as well as a new recurrence for
the derangement numbers.

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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg