Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: {T}he Gr\"obner Basis of a Catalan Path Ideal   For the ideal $I = \langle y_1 + \dots + y_n, y^2_1, \dots , y^2_n \rangle$
in $R = {\mathbb F}[y_1, \dots , y_n]$ with char($\mathbb F$) = 0, we show that
the reduced Gr\"obner basis with lex-order consists of polynomials $g_\alpha$
that are represented in terms of paths, moving northeast in the Cartesian
plane, that stay above the diagonal and cross the diagonal at the last step.
This implies that a linear basis for the quotient ring $R/I$ is given by a set
of Catalan paths. We show that the dimension is the number of standard Young
tableaux of size $n$ and height at most two. The graded Frobenius
characteristic of $R/I$ as a symmetric group module is given by
  $\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor } s_{n-k,k}q^k$.

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The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph