Significance of Knotted Structures for Function of Proteins and Nucleic Acids
Poster Session I
24 – POS
Board 24
A Combinatorial Interpretation of the
Coefficients
Thomas J. X. Li
, Christian M. Reidys
Institut for Matematik og Datalogi, University of Southern Denmark, Denmark
Unicellular map and its shape have been applied to RNA pseudoknotted structure filtered by its
topological genus. Studying the virtual Euler characteristic of the moduli space of curves, Harer
and Zagier compute the generating function
of unicellular maps of genus
g
. They
furthermore identify coefficients,
, which fully determine the series
. The main result of
this abstract is a combinatorial interpretation of
. We show that these enumerate a class of
unicellular maps, which correspond 1-to-
to a specific type of trees, referred to as O-trees, see
Figure 1. We show how to generate from this specific class of O-trees to the class of shapes, see
Figure 2. We prove the
are positive integers that satisfy a two term recursion
We furthermore prove that for any fixed
g
, the sequence
is log-concave, where
,
for
.
Keywords
: unicellular map, fatgraph, O-tree, shape-polynomial, recursion
Figure 1. Figure 2.
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