Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The total run length of a word   A run in a word is a periodic factor whose length is at least twice its
period and which cannot be extended to the left or right (by a letter) to a
factor with greater period. In recent years a great deal of work has been done
on estimating the maximum number of runs that can occur in a word of length
$n$. A number of associated problems have also been investigated. In this paper
we consider a new variation on the theme. We say that the total run length
(TRL) of a word is the sum of the lengths of the runs in the word and that
$\tau(n)$ is the maximum TRL over all words of length $n$. We show that $n^2/8
< \tau(n) < 47n^2/72 + 2n$ for all $n$. We also give a formula for the average
total run length of words of length $n$ over an alphabet of size $\alpha$, and
some other results.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess