Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Staircase patterns in words: subsequences, subwords, and separation
  number   We revisit staircases for words and prove several exact as well as asymptotic
results for longest left-most staircase subsequences and subwords and staircase
separation number, the latter being defined as the number of consecutive
maximal staircase subwords packed in a word. We study asymptotic properties of
the sequence $h_{r,k}(n),$ the number of $n$-array words with $r$ separations
over alphabet $[k]$ and show that for any $r\geq 0,$ the growth sequence
$\big(h_{r,k}(n)\big)^{1/n}$ converges to a characterized limit, independent of
$r.$ In addition, we study the asymptotic behavior of the random variable
$\mathcal{S}_k(n),$ the number of staircase separations in a random word in
$[k]^n$ and obtain several limit theorems for the distribution of
$\mathcal{S}_k(n),$ including a law of large numbers, a central limit theorem,
and the exact growth rate of the entropy of $\mathcal{S}_k(n).$ Finally, we
obtain similar results, including growth limits, for longest $L$-staircase
subwords and subsequences.

36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex