Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schur positivity and log-concavity related to longest increasing
  subsequences   Chen proposed a conjecture on the log-concavity of the generating function
for the symmetric group with respect to the length of longest increasing
subsequences of permutations. Motivated by Chen's log-concavity conjecture,
B\'{o}na, Lackner and Sagan further studied similar problems by restricting the
whole symmetric group to certain of its subsets. They obtained the
log-concavity of the corresponding generating functions for these subsets by
using the hook-length formula. In this paper, we generalize and prove their
results by establishing the Schur positivity of certain symmetric functions.
This also enables us to propose a new approach to Chen's original conjecture.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat