Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On flushed partitions and concave compositions   In this work, we give combinatorial proofs for generating functions of two
problems, i.e., flushed partitions and concave compositions of even length. We
also give combinatorial interpretation of one problem posed by Sylvester
involving flushed partitions and then prove it. For these purposes, we first
describe an involution and use it to prove core identities. Using this
involution with modifications, we prove several problems of different nature,
including Andrews' partition identities involving initial repetitions and
partition theoretical interpretations of three mock theta functions of third
order $f(q)$, $\phi(q)$ and $\psi(q)$. An identity of Ramanujan is proved
combinatorially. Several new identities are also established.

18
The categories of this paper are: econ
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs