Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long twins in random words   Twins in a finite word are formed by a pair of identical subwords placed at
disjoint sets of positions. We investigate the maximum length of twins in a
random word over a $k$-letter alphabet. The obtained lower bounds for small
values of $k$ significantly improve the best estimates known in the
deterministic case. Bukh and Zhou in 2016 showed that every ternary word of
length $n$ contains twins of length at least $0.34n$. Our main result, with a
computer-assisted proof, states that in a random ternary word of length $n$,
with high probability, one can find twins of length at least $0.41n$. In the
general case, for alphabets of size $k\geq 3$, we get analogous lower bounds of
the form $\frac{1.64}{k+1}n$, which are better than the known deterministic
bounds for $k\leq 354$. In addition, we present similar results for multiple
twins in random words.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga