Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Searching Zimin Patterns   In the area of pattern avoidability the central role is played by special
words called Zimin patterns. The symbols of these patterns are treated as
variables and the rank of the pattern is its number of variables. Zimin type of
a word $x$ is introduced here as the maximum rank of a Zimin pattern matching
$x$. We show how to compute Zimin type of a word on-line in linear time.
Consequently we get a quadratic time, linear-space algorithm for searching
Zimin patterns in words. Then we how the Zimin type of the length $n$ prefix of
the infinite Fibonacci word is related to the representation of $n$ in the
Fibonacci numeration system. Using this relation, we prove that Zimin types of
such prefixes and Zimin patterns inside them can be found in logarithmic time.
Finally, we give some bounds on the function $f(n,k)$ such that every $k$-ary
word of length at least $f(n,k)$ has a factor that matches the rank $n$ Zimin
pattern.

33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn