Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles   We present a recursive formula for the number of ways to color $j$ vertices
blue in an r-uniform hyperpath of size $n$ while avoiding a blue monochromatic
sub-hyperpath of length k. We use this result to solve the corresponding
problem for $(r-1)$-tight r-uniform paths and loose r-uniform cycles. This
generalizes some well known results from reliability engineering and analysis.

21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ