Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Pieri-type formula and a factorization formula for sums of
  $K$-$k$-Schur functions   We give a Pieri-type formula for the sum of $K$-$k$-Schur functions
$\sum_{\mu\le\lambda} g^{(k)}_{\mu}$ over a principal order ideal of the poset
of $k$-bounded partitions under the strong Bruhat order, which sum we denote by
$\widetilde{g}^{(k)}_{\lambda}$. As an application of this, we also give a
$k$-rectangle factorization formula
$\widetilde{g}^{(k)}_{R_t\cup\lambda}=\widetilde{g}^{(k)}_{R_t}
\widetilde{g}^{(k)}_{\lambda}$ where $R_t=(t^{k+1-t})$, analogous to that of
$k$-Schur functions $s^{(k)}_{R_t\cup\lambda}=s^{(k)}_{R_t}s^{(k)}_{\lambda}$.

9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas