Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kostka Numbers and Longest Increasing Subsequences   A classical bijection relates certain Kostka numbers, the Catalan numbers,
and permutations of length $n$ with longest increasing subsequence (LIS) of
length at most $2.$ We generalize this bijection and find Kostka numbers which
count the number of permutations of $n$ with LIS length at most $w,$ the number
of permutations with $(1, \cdots, w)$ as a LIS, and other similar subsets of
permutations.

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin