Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal and Multi-Fractal Analysis for A Family of Subset Sum Functions:
  Combinatorial Structures of Embedding Dimension $1$   We introduce two frameworks in order to deal with fractal and multi-fractal
analysis for subset sum problems where some embedding into the $1$-dimensional
Euclidean space plays an important role. As one of these frameworks, the notion
of the combinatorial $q$-fractal dimension for a subset sum function is
introduced. Thereby, ``non-classical'' generalized dimensions for a family of
subset~sum functions can be defined. These generalized dimensions include the
box-counting dimension, the information dimension and the correlation dimension
as well as the classical case. The combinatorial $q$-fractal dimension includes
the density of the subset sum problem. As the other framework, we construct a
self-similar set for a particular subset sum function in a family of subset sum
functions by using a graph theoretical technique.
  In this paper, we give a lower bound for a combinatorial $q$-fractal
dimension and we show the relations between the three parameters: the number of
connected components in a graph, the Hausdorff dimension and a combinatorial
$q$-fractal dimension.

19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an