منابع مشابه
Bipolar orientations Revisited
Acyclic orientations with exactly one source and one sink ~ the so-called bipolar orientations _ arise in many graph algorithms and specially in graph drawing. The fundamental properties of these orientations are explored in terms of circuits, cocircuits and also in terms of “angles” in the planar case. Classical results get here new simple proofs; new results concern the extension of partial o...
متن کاملBijective counting of plane bipolar orientations
We introduce a bijection between plane bipolar orientations with fixed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with some specific extremities. Writing θij for the number of plane bipolar orientations with (i+1) vertices and (j+1) faces, our bijection provides a combinatorial proof of the following formula due to Baxter: θij = 2 (i+ j − 2)! (i+ j − 1)...
متن کاملBaxter permutations and plane bipolar orientations
We present a simple bijection between Baxter permutations of size n and plane bipolar orientations with n edges. This bijection translates several classical parameters of permutations (number of ascents, right-to-left maxima, left-to-right minima...) into natural parameters of plane bipolar orientations (number of vertices, degree of the sink, degree of the source...), and has remarkable symmet...
متن کاملBipolar orientations on planar maps and SLE12
We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the “peano curve” surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a √ 4/3-Liouville quantum gravity surface decorated by an independ...
متن کاملBijective counting of plane bipolar orientations and Schnyder woods
A bijection Φ is presented between plane bipolar orientations with prescribed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with prescribed extremities. This yields a combinatorial proof of the following formula due to R. Baxter for the number Θij of plane bipolar orientations with i non-polar vertices and j inner faces: Θij = 2 (i+ j)! (i+ j + 1)! (i + j ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1995
ISSN: 0166-218X
DOI: 10.1016/0166-218x(94)00085-r