Boolean complexes for Ferrers graphs
نویسندگان
چکیده
In this paper we provide an explicit formula for calculating the boolean number of a Ferrers graph. By previous work of the last two authors, this determines the homotopy type of the boolean complex of the graph. Specializing to staircase shapes, we show that the boolean numbers of the associated Ferrers graphs are the Genocchi numbers of the second kind, and obtain a relation between the Legendre-Stirling numbers and the Genocchi numbers of the second kind. In another application, we compute the boolean number of a complete bipartite graph, corresponding to a rectangular Ferrers shape, which is expressed in terms of the Stirling numbers of the second kind. Finally, we analyze the complexity of calculating the boolean number of a Ferrers graph using these results and show that it is a significant improvement over calculating by edge recursion.
منابع مشابه
ar X iv : 0 80 8 . 23 07 v 1 [ m at h . C O ] 1 7 A ug 2 00 8 BOOLEAN COMPLEXES FOR FERRERS GRAPHS
Ferrers graphs are bipartite graphs that correspond naturally to Ferrers shapes. In this paper, we determine the homotopy type of the boolean complex of Ferrers graphs. Previous work of the last two authors shows that the boolean complex of a graph is a wedge of spheres of maximal dimension. Thus the homotopy type of this complex depends entirely on the number of spheres in the wedge sum, calle...
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 48 شماره
صفحات -
تاریخ انتشار 2010