@inbook{b2e017479beb4ad5b81463898534524d,
title = "On the Enumeration of Plane Bipolar Posets and Transversal Structures",
abstract = "We show that plane bipolar posets (i.e., plane bipolar orientations with no transitive edge) and transversal structures can be set in correspondence to certain (weighted) models of quadrant walks, via suitable specializations of a bijection due to Kenyon, Miller, Sheffield and Wilson. We then derive exact and asymptotic counting results, and in particular we prove that the number tn of transversal structures on n+ 2 vertices satisfies (for some c> 0 ) tn∼c(27/2)nn-1-π/arccos(7/8), which also ensures that the associated generating function is not D-finite.",
keywords = "Bijections, Oriented planar maps, Quadrant walks",
author = "{\'E}ric Fusy and Erkan Narmanli and Gilles Schaeffer",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2021",
month = jan,
day = "1",
doi = "10.1007/978-3-030-83823-2\_90",
language = "English",
series = "Trends in Mathematics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "560--566",
booktitle = "Trends in Mathematics",
}