On the number of crossing-free partitions
نویسندگان
چکیده
منابع مشابه
Free Probability Theory and Non-crossing Partitions
Voiculescu's free probability theory { which was introduced in an operator algebraic context, but has since then developed into an exciting theory with a lot of links to other elds { has an interesting combinatorial facet: it can be described by the combinatorial concept of multiplicative functions on the lattice of non-crossing partitions. In this survey I want to explain this connection { wit...
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of Kirkman (first proven by Cayley; see [7]) for the number of dissections of an n-gon using d diagonals. The goal here is to generalize Bóna’s result to count 1-crossing partitions by their number of blocks, and also to examine a natural q-analogue with regard to the cyclic sieving phenomenon shown in [8] for certain q-Catalan and q-Narayana numbers. The crux is the observation that 1-crossing...
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The material gives a new combinatorial proof of the multiplicative property of the S-transform. In particular, several properties of the coefficients of its inverse are connected to non-crossing linked partitions and planar trees. AMS subject classification: 05A10 (Enumerative Combinatorics); 46L54(Free Probability and Free Operator Algebras).
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This is one of the survey talks at the workshop on “Braid groups, clusters, and free probability” at the American Institute of Mathematics, January 10-14, 2005. The goal of the talk is to give a quick and elementary introduction to some combinatorial aspects of free probability, addressed to an audience who is not familiar with free probability but is acquainted to lattices of non-crossing part...
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Research about crossings is typically about minimization. In this paper, we consider maximizing the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [1] conjectured that any graph has a convex straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructin...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2013
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2011.07.001