Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure of Binary Sequences   The distribution of a given sequence in the set of all sequences with n ones
and m = M - n zeros are found by relating the problem to the partitions of a
natural number in m natural summands, taking into account the order. The
formulas obtained have many applications both in Physics and Mathematics.
Examples discussed in the present paper are: non Markovian chains, partition
functions of binary alloys and Ising magnets, generalized Kaplansky lemma,
generalized Fibonacci numbers and a general expansion of \sum_{h=0}^{m} h^{r}
{\binom{m}{h}}^{2} in terms of the Stirling numbers of second kind.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
1
The categories of this paper are: cs
19
The categories of this paper are: eess
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph