Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic structure representations for lattices   For an arbitrary group, the subgroups form a lattice with order determined by
set inclusion. Not every lattice is isomorphic to the subgroup lattice for a
group. However, Birkhoff and Frink proved that any compactly generated lattice
is isomorphic to a subalgebra lattice for some algebraic structure. An
algebraic structure is a set A with operations from A^n to A where n$is a
non-negative integer. Although the proof by Birkhoff and Frink is constructive,
many of the operations described are not needed for an algebraic structure to
represent a given lattice. In this paper we utilize concepts in the proof by
Birkhoff and Frink to describe and count functions that are used to create
algebraic structure representations for certain finite lattice types.

30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex