Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new polynomial on compositions of integers: on distinguishing
  caterpillars from their symmetric chromatic function   In this paper, we propose an algebraic approach to determine whether two
non-isomorphic caterpillar trees can have the same symmetric function
generalization of the chromatic polynomial. On the set of all composition on
integers, we introduce: An operation, which we call composition product; and a
combinatorial polynomial, which we call the composition-lattice polynomial or
L-polynomial, that mimics the weighted graph polynomial of Noble and Welsh. We
prove a unique irreducible factorization theorem and establish a connection
between the L-polynomial of a composition and its irreducible factorization,
namely that reversing irreducible factors does not change L, and conjecture
that is the only way of generating such compositions. Finally, we find a
sufficient condition for two caterpillars have a different symmetric function
generalization of the chromatic polynomial, and use this condition to show that
if our conjecture were to hold, then the symmetric function generalization of
the chromatic polynomial distinguishes among a large class of caterpillars.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys