Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The forgotten monoid   We study properties of the forgotten monoid which appeared in work of Lascoux
and Schutzenberger and recently resurfaced in the construction of dual
equivalence graphs by Assaf. In particular, we provide an explicit
characterization of the forgotten classes in terms of inversion numbers and
show that there are n^2-3n+4 forgotten classes in the symmetric group S_n. Each
forgotten class contains a canonical element that can be characterized by
pattern avoidance. We also show that the sum of Gessel's quasi-symmetric
functions over a forgotten class is a 0-1 sum of ribbon-Schur functions.

35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph