منابع مشابه
The colorful language of Australian flowers
The enormous increase in phylogenetic information in recent years has allowed many old questions to be reexamined from a macroevolutionary perspective. We have recently considered evolutionary convergence in floral colors within pollination syndromes, using bird-pollinated species in Australia. We combined quantitative measurements of floral reflectance spectra, models of avian color vision, an...
متن کاملColorful Strips
We study the following geometric hypergraph coloring problem: given a planar point set and an integer k, we wish to color the points with k colors so that any axis-aligned strip containing sufficiently many points contains all colors. We show that if the strip contains at least 2k−1 points, such a coloring can always be found. In dimension d, we show that the same holds provided the strip conta...
متن کاملColorful Curvature
Nonlinearities provide a neverending challenge to systems and control. We savor linear systems since we have a good understanding of how they behave, and there is much we can do to analyze and predict their performance. As we move away from linearity, we need to scrutinize each nonlinearity that we encounter to assess its benefi t or detriment in terms of what we wish to achieve. The first issu...
متن کاملThe Colorful Helly Theorem and Colorful Resolutions of Ideals
We demonstrate that the topological Helly theorem and the algebraic Auslander-Buchsbaum may be viewed as different versions of the same phenomenon. Using this correspondence we show how the colorful Helly theorem of I.Barany and its generalizations by G.Kalai and R.Meshulam translates to the algebraic side. Our main results are algebraic generalizations of these translations, which in particula...
متن کاملMaking Triangles Colorful
We prove that for any finite point set P in the plane, a triangle T , and a positive integer k, there exists a coloring of P with k colors such that any homothetic copy of T containing at least 144k8 points of P contains at least one of each color. This is the first polynomial bound for range spaces induced by homothetic polygons. The only previously known bound for this problem applies to the ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2009
ISSN: 0166-8641
DOI: 10.1016/j.topol.2008.12.013