Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A symmetric chain decomposition of $N(m,n)$ of composition   A poset is called a symmetric chain decomposition if the poset can be
expressed as a disjoint union of symmetric chains. For positive integers $m$
and $n$, let $N(m,n)$ denote the set of all compositions
$\alpha=(\alpha_1,\cdots,\alpha_m)$, with $0\le \alpha_i \le n$ for each
$i=1,\cdots,m$. Define order $<$ as follow, $\forall \alpha,\beta \in N(m,n)$,
$\beta < \alpha$ if and only if $\beta_i \le \alpha_i(i=1,\cdots,m)$ and
$\sum\limits_{i=1}^{m}\beta_i <\sum\limits_{i=1}^{m}\alpha_i$. In this paper,
we show that the poset $(N(m,n),<)$ can be expressed as a disjoint of symmetric
chains by constructive method.

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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
16
The categories of this paper are: stat