Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of simultaneous core partitions   Amdeberhan conjectured that the number of $(t,t+1, t+2)$-core partitions is
$\sum_{0\leq k\leq [\frac{t}{2}]}\frac{1}{k+1}\binom{t}{2k}\binom{2k}{k}$. In
this paper, we obtain the generating function of the numbers $f_t$ of $(t, t +
1, ..., t + p)$-core partitions. In particular, this verifies that Amdeberhan's
conjecture is true. We also prove that the number of $(t_1,t_2,..., t_m)$-core
partitions is finite if and only if gcd$(t_1,t_2,..., t_m)=1,$ which extends
Anderson's result on the finiteness of the number of $(t_1,t_2)$-core
partitions for coprime positive integers $t_1$ and $t_2$ and thus rediscover a
result of Keith and Nath with a different proof.

5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics