Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three Results on Making Change (An Exposition)   Assume you an infinite supply of pennies, nickels, dimes, and quarters (or
some other finite set of denominations which are relatively prime). Let CH(n)
be the number of ways to make change of n cents. We present a simple unified
exposition of three know theorems about CH(n). Let M be the LCM of a1,...,aL.
Let M' be the LCM of the GCD of all pairs of ai's. (1) If 0\le r\le M-1 then
CH(n) restricted to n \equiv r mod M is a poly, (2) If 0\le r\le M'-1 then
CH(n) restricted to n\equiv r mod M' is a poly except for the constant term,
(3) CH(n) is n^{L-1}/(L-1)!a1a2...aL + O(n^{L-2}). Part (3) is known as Schur's
theorem.

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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci