Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Recursion for the FiboNarayana and the Generalized Narayana Numbers   The Lucas polynomials, $\{n\}$, are polynomials in $s$ and $t$ given by $\{ n
\} = s \{ n-1 \} + t \{ n-2 \}$ for $n \geq 2$ with $ \{ 0 \} = 0$ and $\{ 1 \}
= 1$. The lucanomial coefficients, an analogue of the binomial coefficients,
are given by \[ \Bigl\{ \begin{array}{c} n\\k \end{array} \Bigr \} = \frac{
\{n\}! }{ \{k\}! \{n-k\}!}. \] When $s = t = 1$ then $\{ n \} = F_n$ and the
lucanomial coefficient becomes the fibonomial coefficient \[ \binom{n}{k}_F =
\frac{F_n!}{F_k! F_{n-k}!}. \] The well-known Narayana numbers, $N_{n,k}$
satisfy the equation \[ N_{n,k} = \frac{1}{n} \binom{n}{k} \binom{n}{k-1}. \]
  \[ %C_n = \sum_{k=1}^n N_{n,k}. %\] In 2018, Bennett, Carrillo, Machacek and
Sagan defined the generalized Narayana numbers and conjectured that these
numbers are positive integers for $n \geq 1$. In this paper we define the
FiboNarayana number $N_{n,k,F}$ and give a new recurrence relation for both the
FiboNarayana numbers and the generalized Narayana numbers, proving the
conjecture that these are positive integers for $n \geq 1$.

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The categories of this paper are: bayes-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: econ