Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the expansion of three-element subtraction sets   We study the periodicity of nim-sequences for subtraction games having
subtraction sets with three elements. In particular, we give solutions in
several cases, and we describe how these subtraction sets can be augmented by
additional numbers without changing the nim-sequences. The paper concludes with
a conjecture on ultimately bipartite subtraction games.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph