Colored partitions of a convex polygon by noncrossing diagonals
نویسندگان
چکیده
منابع مشابه
Note on noncrossing path in colored convex sets ∗
Consider a 2n element colored point set, n points red and n points blue, in convex position in the plane. Erdős asked to estimate the number of points in the longest noncrossing path such that edges join points of different color and are straight line segments. Kynčl, Pach and Tóth in 2008 gave a construction proving the upper bound 43n+ O( √ n). This bound is conjectured to be tight. For an ar...
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In 1973, Victor Klee posed the problem of determining the minimum number of guards sufficient to cover the interior of an n-wall art gallery room (Honsberger 1976). He posed this question extemporaneously in response to a request from Vasek Chvatal (at a conference at Stanford in August) for an interesting geometric problem, and Chvatal soon established what has become known as "Chvatal's Art G...
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Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length 2n and noncrossing partitions of [2n + 1] with n + 1 blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2016.12.006