Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Sprague-Grundy Function of Tetris Extensions of Proper {\sc Nim}   Given a hypergraph $\cH \subseteq 2^I \setminus \{\emptyset\}$ on the ground
set $I = \{1, \ldots, n\}$, we assign to each $i \in I$ a nonnegative integer
$x_i$, that is a pile of $x_i$ tokens, and consider the following
generalization of the classical game of {\sc Nim}: Two players alternate turns.
In a move a player chooses an arbitrary edge $H \in \cH$ and reduces all piles
$i \in H$. The player who is out of moves loses. We call the obtained game
hypergraph {\sc Nim}. Such a game is called proper {\sc Nim}, when $\cH=2^I
\setminus\{I,\emptyset\}$ is the family of all proper subsets of $I$. Jenkyns
and Mayberry \cite{JM80} described the Sprague-Grundy (or SG in short) function
of these games. In this paper we introduce Tetris extensions of hypergraph {\sc
Nim}, and obtain a closed formula for the SG functions of the extensions of
proper {\sc Nim}, when $n\geq 3$. Surprisingly, the case of $n=2$ is much more
complicated. For this case we only suggest several partial results and
conjectures.

28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin