Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorisation of Greedoid Polynomials of Rooted Digraphs   Gordon and McMahon defined a two-variable greedoid polynomial $ f(G;t,z) $
for any greedoid $ G $. They studied greedoid polynomials for greedoids
associated with rooted graphs and rooted digraphs. They proved that greedoid
polynomials of rooted digraphs have the multiplicative direct sum property. In
addition, these polynomials are divisible by $ 1 + z $ under certain
conditions. We compute the greedoid polynomials for all rooted digraphs up to
order six. A greedoid polynomial $ f(D) $ of a rooted digraph $ D $ of order $
n $ GM-factorises if $ f(D) = f(G) \cdot f(H) $ such that $ G $ and $ H $ are
rooted digraphs of order at most $ n $ and $ f(G),f(H) \ne 1 $. We study the
GM-factorability of greedoid polynomials of rooted digraphs, particularly those
that are not divisible by $ 1 + z $. We give some examples and an infinite
family of rooted digraphs that are not direct sums but their greedoid
polynomials GM-factorise.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int