Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice paths and branched continued fractions: An infinite sequence of
  generalizations of the Stieltjes--Rogers and Thron--Rogers polynomials, with
  coefficientwise Hankel-total positivity   We define an infinite sequence of generalizations, parametrized by an integer
$m \ge 1$, of the Stieltjes--Rogers and Thron--Rogers polynomials; they arise
as the power-series expansions of some branched continued fractions, and as the
generating polynomials for $m$-Dyck and $m$-Schr\"oder paths with
height-dependent weights. We prove that all of these sequences of polynomials
are coefficientwise Hankel-totally positive, jointly in all the (infinitely
many) indeterminates. We then apply this theory to prove the coefficientwise
Hankel-total positivity for combinatorially interesting sequences of
polynomials. Enumeration of unlabeled ordered trees and forests gives rise to
multivariate Fuss--Narayana polynomials and Fuss--Narayana symmetric functions.
Enumeration of increasing (labeled) ordered trees and forests gives rise to
multivariate Eulerian polynomials and Eulerian symmetric functions, which
include the univariate $m$th-order Eulerian polynomials as specializations. We
also find branched continued fractions for ratios of contiguous hypergeometric
series ${}_r \! F_s$ for arbitrary $r$ and $s$, which generalize Gauss'
continued fraction for ratios of contiguous ${}_2 \! F_1$; and for $s=0$ we
prove the coefficientwise Hankel-total positivity. Finally, we extend the
branched continued fractions to ratios of contiguous basic hypergeometric
series ${}_r \! \phi_s$.

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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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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: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph