Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial results on $t$-cores and sums of squares   We classify the connection between $t$-cores and self-conjugate $t$-cores to
sums of squares. To do so, we provide explicit maps between $t$-core partitions
and self-conjugate $t$-core partitions of a positive integer $n$ to
representations of certain numbers as sums of squares. For example, the
self-conjugate $4$-core partition $\lambda=(4,1,1,1)$ corresponds uniquely to
the solution $61=6^2+5^2$. As a corollary, we completely classify the
relationship between $t$-cores and Hurwitz class numbers.
  Using these tools, we see how certain sets of representations as sums of
squares naturally decompose into families of $t$-cores. Finally, we construct
an explicit map on partitions to explain the equality
$2\operatorname{sc}_7(8n+1) = \operatorname{c}_4(7n+2)$ previously studied by
Bringmann, Kane, and the first author.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph