Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Matrix polynomials of Tree Laplacians indexed by Symmetric
  functions and the GTS poset   Let $T$ be a tree on $n$ vertices with $q$-Laplacian $L_T^q$ and Laplacian
matrix $L_T$. Let $GTS_n$ be the generalized tree shift poset on the set of
unlabelled trees on $n$ vertices. Inequalities are known between coefficients
of the immanantal polynomial of $L_T$ (and $L_T^q$) as we go up the poset
$GTS_n$. Using the Frobenius characteristic, this can be thought as a result
involving the schur symmetric function $s_{\lambda}$. In this paper, we use an
arbitrary symmetric function to define a {\it generalized matrix function} of
an $n \times n$ matrix. When the symmetric function is the monomial and the
forgotten symmetric function, we generalize such inequalities among
coefficients of the generalized matrix polynomial of $L_T^q$ as we go up the
$GTS_n$ poset.

13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat