Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of combinations without certain separations   In this paper we enumerate the number of ways of selecting $k$ objects from
$n$ objects arrayed in a line such that no two selected ones are separated by
$m-1,2m-1,...,pm-1$ objects and provide three different formulas when $m,p\geq
1$ and $n\geq pm(k-1)$. Also, we prove that the number of ways of selecting $k$
objects from $n$ objects arrayed in a circle such that no two selected ones are
separated by $m-1,2m-1,...,pm-1$ objects is given by
$\frac{n}{n-pk}\binom{n-pk}{k}$, where $m,p\geq 1$ and $n\geq mpk+1$.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph