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Discrepancy, Hereditary and Linear counterparts
In this note we will talk about linear and hereditary discrepancy. For the basic definition of discrepancy, please refer to this article. Let be a set system with and . Let be its incidence matrix, i.e. otherwise. This matrix captures lots of structural information about the set system. It is, for example easy to see… — read more
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Colorful Carathéodory theorem
In this post, we will talk about a colorful version of the classical Carathéodory’s theorem due to Imre Bárány. I recently read about it, thought that it would be nice to present the proof of it, which is interesting. The classical Carathéodory’s theorem states that if a point lies in the convex hull of a… — read more
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Some properties of Error function and its inverse in connection to Normal cdf
Normal distribution is ubiquitous in physics, engineeering and mathematics. It is a continuous distribution for a real values random variable. The central limit theorem roughly states that the distribution of properly scaled average of many samples, taken from a distribution with finite mean and variance converges to Normal distribution. This distribution also plays a crucial… — read more
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On the Beck-Fiala theorem
The Beck-Fiala Theorem says that, if a finite hypergraph has bounded degree, the discreapancy of the hypergraph can be bounded by some function depending only on its degree. The proof of this theorem uses very simple facts of linear algebra and yields an efficient algorithm that finds a coloring matching the bound. What is discrepancy?… — read more
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A certain equivalence of the maximum flow problem and the problem of minimizing maximum congestion of a unit flow
This is my first blog post. Throughout the post we assume to be the number of vertices in the graph and to be the number of edges. Consider an undirected graph , where each edge has a non negative capacity . A flow is vector in that satisfies the flow conservation property. It is feasible… — read more
"The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree"
sudipta1411 