Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics   Prudent walks are special self-avoiding walks that never take a step towards
an already occupied site, and \emph{$k$-sided prudent walks} (with $k=1,2,3,4$)
are, in essence, only allowed to grow along $k$ directions. Prudent polygons
are prudent walks that return to a point adjacent to their starting point.
Prudent walks and polygons have been previously enumerated by length and
perimeter (Bousquet-M\'elou, Schwerdtfeger; 2010). We consider the enumeration
of \emph{prudent polygons} by \emph{area}. For the 3-sided variety, we find
that the generating function is expressed in terms of a $q$-hypergeometric
function, with an accumulation of poles towards the dominant singularity. This
expression reveals an unusual asymptotic structure of the number of polygons of
area $n$, where the critical exponent is the transcendental number $\log_23$
and and the amplitude involves tiny oscillations. Based on numerical data, we
also expect similar phenomena to occur for 4-sided polygons. The asymptotic
methodology involves an original combination of Mellin transform techniques and
singularity analysis, which is of potential interest in a number of other
asymptotic enumeration problems.

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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an