Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial aspects of the conserved quantities of the tropical
  periodic Toda lattice   The tropical periodic Toda lattice (trop p-Toda) is a dynamical system
attracting attentions in the area of the interplay of integrable systems and
tropical geometry. We show that the Young diagrams associated with trop p-Toda
given by two very different definitions are identical. The first definition is
given by a Lax representation of the discrete periodic Toda lattice, and the
second one is associated with a generalization of the
Kerov-Kirillov-Reshetikhin bijection in the combinatorics of the Bethe ansatz.
By means of this identification, it is shown for the first time that the Young
diagrams given by the latter definition are preserved under time evolution.
This result is regarded as an important first step in clarifying the iso-level
set structure of this dynamical system in general cases, i.e. not restricted to
generic cases.

28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex