منابع مشابه
Coloring Non-Crossing Strings
For a family of geometric objects in the plane F = {S1, . . . , Sn}, define χ(F) as the least integer ` such that the elements of F can be colored with ` colors, in such a way that any two intersecting objects have distinct colors. When F is a set of pseudo-disks that may only intersect on their boundaries, and such that any point of the plane is contained in at most k pseudo-disks, it can be p...
متن کاملEnumeration of non-crossing pairings on bit strings
A non-crossing pairing on a bitstring matches 1s and 0s in a manner such that the pairing diagram is nonintersecting. By considering such pairings on arbitrary bitstrings 1101 . . . 1r0r , we generalize classical problems from the theory of Catalan structures. In particular, it is very difficult to find useful explicit formulas for the enumeration function φ(n1, m1, . . . , nr, mr), which count...
متن کاملColoring a set of touching strings
For a family of geometric objects in the plane F = {S1, . . . , Sn}, define χ(F) as the least integer l such that the elements of F can be colored with l colors, in such a way that any two intersecting objects have distinct colors. When F is a set of Jordan regions that may only intersect on their boundaries, and such that any point of the plane is contained in at most k regions, it can be prov...
متن کاملNon-Crossing Frameworks with Non-Crossing Reciprocals
We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing frameworks G whose reciprocals are non-crossing, in terms of: the types of faces (only pseudo-triangles and pseudo-quadrangles are allowed); the sign patterns in the stress on G; and a geometric condition on ...
متن کاملOn the Enumeration of Non-crossing Pairings of Well-balanced Binary Strings
A non-crossing pairing on a binary string pairs ones and zeroes such that the arcs representing the pairings are non-crossing. A binary string is well-balanced if it is of the form 11011202 . . . 1r0r . In this paper we establish connections between non-crossing pairings of well-balanced binary strings and various lattice paths in plane. We show that for well-balanced binary strings with a1 ≤ a...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5710