Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circular Nim CN(7,4)   Circular Nim is a two-player impartial combinatorial game consisting of $n$
stacks of tokens placed in a circle. A move consists of choosing $k$
consecutive stacks and taking at least one token from one or more of the
stacks. The last player able to make a move wins. The question of interest is:
Who can win from a given position if both players play optimally? In an
impartial combinatorial game, there are only two types of positions. An
$\mathcal{N}$-position is one from which the next player to move has a winning
strategy. A $\mathcal{P}$-position is one from which the next player is bound
to lose, no matter what moves s/he makes. Therefore, the question who wins is
answered by identifying the $\mathcal{P}$-positions. We will prove results on
the structure of the $\mathcal{P}$-positions for $n = 7$ and $k = 4$, extending
known results for other games in this family. The interesting feature of the
set of $\mathcal{P}$-positions of this game is that it splits into different
subsets, unlike the structure for the known games in this family.

1
The categories of this paper are: cs
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg