Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slit-slide-sew bijections for bipartite and quasibipartite plane maps   We unify and extend previous bijections on plane quadrangulations to
bipartite and quasibipartite plane maps. Starting from a bipartite plane map
with a distinguished edge and two distinguished corners (in the same face or in
two different faces), we build a new plane map with a distinguished vertex and
two distinguished half-edges directed toward the vertex. The faces of the new
map have the same degree as those of the original map, except at the locations
of the distinguished corners, where each receives an extra degree. The idea
behind this bijection is to build a path from the distinguished elements, slit
the map along it, and sew back after sliding by one unit, thus mildly modifying
the structure of the map at the extremities of the sliding path. This bijection
provides a sampling algorithm for uniform maps with prescribed face degrees and
allow to recover Tutte's famous counting formula for bipartite and
quasibipartite plane maps.
  In addition, we explain how to decompose the previous bijection into two more
elementary ones, which each transfer a degree from one face of the map to
another face. In particular, these transfer bijections are simpler to
manipulate than the previous one and this point of view simplifies the proofs.

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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th